In the fractional quantum Hall effect ~FQHE! The dissipative response of a quantum system upon a time-dependent drive can be exploited as a probe of its geometric and topological properties. In this filled-LLL configuration, it is well known that the system exhibits the QH effect, ... Its construction is simple , yet its implication is rich. a GaAs-GaAlAs heterojunction. Therefore, an anyon, a particle that has intermediate statistics between Fermi and Bose statistics, can exist in two-dimensional space. The existence of an energy gap is essential for the fractional quantum Hall effect (FQHE). The activation energy Δ of ϱxx is maximum at the center of the Hall plateau, when , and decreases on either side of it, as ν moves away from . <>/XObject<>/Font<>/Pattern<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 2592 1728] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> It is shown that a filled Landau level exhibits a quantized circular dichroism, which can be traced back to its underlying non-trivial topology. About this book. 2 0 obj The so-called composite fermions are explained in terms of the homotopy cyclotron braids. electron system with 6×1010 cm-2 carriers in The fractional quantum Hall effect is the result of the highly correlated motion of many electrons in 2D ex-posed to a magnetic field. This effect, termed the fractional quantum Hall effect (FQHE), represents an example of emergent behavior in which electron interactions give rise to collective excitations with properties fundamentally distinct from the fractal IQHE states. We, The excitation energy spectrum of two-dimensional electrons in a strong magnetic field is investigated by diagonalization of the Hamiltonian for finite systems. The experimental discovery of the fractional quantum Hall effect (FQHE) at the end of 1981 by Tsui, Stormer and Gossard was absolutely unexpected since, at this time, no theoretical work existed that could predict new struc tures in the magnetotransport coefficients under conditions representing the extreme quantum limit. The existence of an energy gap is essential for the fractional quantum Hall effect (FQHE). Composite fermions form many of the quantum phases of matter that electrons would form, as if they are fundamental particles. As in the integer quantum Hall effect, the Hall resistance undergoes certain quantum Hall transitions to form a series of plateaus. Here we report a transient suppression of bulk conduction induced by terahertz wave excitation between the Landau levels in a GaAs quantum Hall system. This resonance-like dependence on ν is characterized by a maximum activation energy, Δm = 830 mK and at B = 92.5 kG. Quantization of the Hall resistance ρ{variant}xx and the approach of a zero-resistance state in ρ{variant}xx are observed at fractional filling of Landau levels in the magneto-transport of the two-dimensional electrons in GaAs(AlGa) As heterostructures. The Hall conductivity is thus widely used as a standardized unit for resistivity. When the cyclotron energy is not too small compared to a typical Coulomb energy, no qualitative change of the ground state is found: A natural generalization of the liquid state at the infinite magnetic field describes the ground state. Several new topics like anyons, radiative recombinations in the fractional regime, experimental work on the spin-reversed quasi-particles, etc. M uch is understood about the frac-tiona l quantum H all effect. Download PDF Abstract: Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. We shall see that the fractional quantum Hall state can be considered as a Bose-condensed state of bosonized electrons. The logarithm of the overlap, which is a geometric quantity, is then taken as a geometric measure of entanglement. • Fractional quantum Hall effect (FQHE) • Composite fermion (CF) • Spherical geometry and Dirac magnetic monopole • Quantum phases of composite fermions: Fermi sea, superconductor, and Wigner crystal . Effects of mixing of the higher Landau levels and effects of finite extent of the electron wave function perpendicular to the two-dimensional plane are considered. endobj In this strong quantum regime, electrons and magnetic flux quanta bind to form complex composite quasiparticles with fractional electronic charge; these are manifest in transport measurements of the Hall conductivity as rational fractions of the elementary conductance quantum. Quantum Hall Effect Emergence in the Fractional Quantum Hall Effect Abstract Student Luis Ramirez The experimental discovery of the fractional quantum hall effect (FQHE) in 1980 was followed by attempts to explain it in terms of the emergence of a novel type of quantum liquid. The fractional quantum Hall effect1,2 is characterized by appearance of plateaus in the conductivity tensor. Theory of the Integer and Fractional Quantum Hall Effects Shosuke SASAKI . ���"��ν��m]~(����^ b�1Y�Vn�i���n�!c�dH!T!�;�&s8���=?�,���"j�t�^��*F�v�f�%�����d��,�C�xI�o�--�Os�g!=p�:]��W|�efd�np㭣 +Bp�w����x�! Preface . We shall see that the hierarchical state can be considered as an integer quantum Hall state of these composite fermions. Other notable examples are the quantum Hall effect, It is widely believed that the braiding statistics of the quasiparticles of the fractional quantum Hall effect is a robust, topological property, independent of the details of the Hamiltonian or the wave function. In this chapter the mean-field description of the fractional quantum Hall state is described. At filling 1=m the FQHE state supports quasiparticles with charge e=m [1]. Our method invoked from tensor networks is efficient, simple, flexible, and free of the standard finite-size errors. The numerical results of the spin models on honeycomb and simple cubic lattices show that the ground-state properties including quantum phase transitions and the critical behaviors are accurately captured by only O(10) physical and bath sites. $${\phi _{n,m}}(\overrightarrow r ) = \frac{{{e^{|Z{|^2}/4{l^2}}}}}{{\sqrt {2\pi } }}{G^{m,n}}(iZ/l)$$ (2) The excitation spectrum from these qualitatively different ground, In the previous chapter it was demonstrated that the state that causes the fractional quantum Hall effect can be essentially represented by Laughlin’s wave function. We study numerically the geometric entanglement in the Laughlin wave function, which is of great importance in condensed matter physics. The quasihole states can be stably prepared by pinning the quasiholes with localized potentials and a measurement of the mean square radius of the freely expanding cloud, which is related to the average total angular momentum of the initial state, offers direct signatures of the statistical phase. a plateau in the Hall resistance, is observed in two-dimensional electron gases in high magnetic fields only when the mobile charged excitations have a gap in their excitation spectrum, so the system is incompressible (in the absence of disorder). This work suggests alternative forms of topological probes in quantum systems based on circular dichroism. � �y�)�l�d,�k��4|\�3%Uk��g;g��CK�����H�Sre�����,Q������L"ׁ}�r3��H:>��kf�5 �xW��� Analytical expressions for the degenerate ground state manifold, ground state energies, and gapless nematic modes are given in compact forms with the input interaction and the corresponding ground state structure factors. fractional quantum Hall effect to be robust. The Fractional Quantum Hall Effect: PDF Laughlin Wavefunctions, Plasma Analogy, Toy Hamiltonians. This observation, unexpected from current theoretical models for the quantized Hall effect, suggests the formation of a new electronic state at fractional level occupation. %���� © 2008-2021 ResearchGate GmbH. The fact that something special happens along the edge of a quantum Hall system can be seen even classically. The statistics of a particle can be. The ground state has a broken symmetry and no pinning. The general idea is to embed a small bulk of the infinite model in an “entanglement bath” so that the many-body effects can be faithfully mimicked. The presence of the energy gap at fractional fillings provides a downward cusp in the correlation energy which makes those states stable to produce quantised Hall steps. In the latter, the gap already exists in the single-electron spectrum. We report the measurement, at 0.51 K and up to 28 T, of the ]����$�9Y��� ���C[�>�2RNJ{l5�S���w�o� At the lowest temperatures (T∼0.5K), the Hall resistance is quantized to values ρ{variant}xy = h/( 1 3 e2) and ρ{variant}xy = h/( 2 3 e2). l"֩��|E#綂ݬ���i ���� S�X����h�e�`��� ��F<>�Z/6�ꖗ��ح����=�;L�5M��ÞD�ё�em?��A��by�F�g�ֳ;/ݕ7q��vV�jt��._��yްwZ��mh�9Qg�ޖ��|�F1�C�W]�z����D͙{�I ��@r�T�S��!z�-�ϋ�c�! a quantum liquid to a crystalline state may take place. ., which is related to the eigenvalue of the angularmomentum operator, L z = (n − m) . 1���"M���B+83��D;�4��A8���zKn��[��� k�T�7���W@�)���3Y�I��l�m��I��q��?�t����{/���F�N���`�z��F�=\��1tO6ѥ��J�E�꜆Ś���q�To���WF2��o2�%�Ǎq���g#���+�3��e�9�SY� �,��NJ�2��7�D "�Eld�8��갎��Dnc NM��~�M��|�ݑrIG�N�s�:��z,���v,�QA��4y�磪""C�L��I!�,��'����l�F�ƓQW���j i& �u��G��،cAV�������X$���)u�o�؎�%�>mI���oA?G��+R>�8�=j�3[�W��f~̈́���^���˄:g�@���x߷�?� ?t=�Ɉ��*ct���i��ő���>�$�SD�$��鯉�/Kf���$3k3�W���F��!D̔m � �L�B�!�aZ����n Anyons, Fractional Charge and Fractional Statistics. The fractional quantum Hall effect is a very counter- intuitive physical phenomenon. Fractional quantum Hall effect and duality Dam Thanh Son (University of Chicago) Strings 2017, Tel Aviv, Israel June 26, 2017. The Nobel Prize in Physics 1998 was awarded jointly to Robert B. Laughlin, Horst L. Störmer and Daniel C. Tsui "for their discovery of a new form of quantum fluid with fractionally charged excitations". However, in the case of the FQHE, the origin of the gap is different from that in the case of the IQHE. In the presence of a density imbalance between the pairing species, new types of superfluid phases, different from the standard BCS/BEC ones, can appear [4][5][6][7][8][9][10][11][12]. Rev. It is found that the ground state is not a Wigner crystal but a liquid-like state. Our results demonstrate a new means of effecting dynamical control of topology by manipulating bulk conduction using light. However, in the case of the FQHE, the origin of the gap is different from that in the case of the IQHE. The knowledge of the quasiparticle charge makes extrapolation of the numerical results to infinite momentum possible, and activation energies are obtained. This article attempts to convey the qualitative essence of this still unfolding phenomenon, known as the fractional quantum Hall effect. In the symmetric gauge \((\overrightarrow {\text{A}} = {\text{H}}( - y,x)/2)\) the single-electron kinetic energy operator We shall show that although the statistics of the quasiparticles in the fractional quantum Hall state can be anything, it is most appropriate to consider the statistics to be neither Bose or Fermi, but fractional. Here m is a positive odd integer and N is a normalization factor. PDF. Excitation energies of quasiparticles decrease as the magnetic field decreases. 4 0 obj Here, we demonstrate that the fractional nature of the quantized Hall conductance, a fundamental characteristic of FQH states, could be detected in ultracold gases through a circular-dichroic measurement, namely, by monitoring the energy absorbed by the atomic cloud upon a circular drive. Several properties of the ground state are also investigated. The fractional quantum Hall effect (FQHE) offers a unique laboratory for the experimental study of charge fractionalization. $${\varepsilon _{n,m}} = \overline n {\omega _c}(n + \frac{1}{2})$$ (3). Found only at temperatures near absolute zero and in extremely strong magnetic fields, this liquid can flow without friction. 4. Next, we consider changing the statistics of the electrons. In this work, we explore the implications of such phenomena in the context of two-dimensional gases subjected to a uniform magnetic field. ]�� linearity above 18 T and exhibited no additional features for filling Although the nature of the ground state is still not clear, the magnitude of the cusp is consistent with the experimentally observed anomaly in σxy and σxx at 13 filling by Tsui, Stormer and Gossard (Phys. The results suggest that a transition from The formation of a Wigner solid or charge-density-wave state with triangular symmetry is suggested as a possible explanation. The existence of an anomalous quantized The fractional quantum Hall effect (FQHE), i.e. Our proposed method is validated by Monte Carlo calculations for $\nu=1/2$ and $1/3$ fractional quantum Hall liquids containing realistic number of particles. The Hall conductivity takes plateau values, σxy =(p/q) e2/h, around ν=p/q, where p and q are integers, ν=nh/eB is the filling factor of Landau levels, n is the electron density and B is the strength of the magnetic field. The Slater determinant having the largest overlap with the Laughlin wave function is constructed by an iterative algorithm. It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. The statistics of quasiparticles entering the quantum Hall effect are deduced from the adiabatic theorem. A quantized Hall plateau of ρxy=3h/e2, accompanied by a minimum in ρxx, was observed at T<5 K in magnetotransport of high-mobility, two-dimensional electrons, when the lowest-energy, spin-polarized Landau level is 1/3 filled. <> However, bulk conduction could also be suppressed in a system driven out of equilibrium such that localized states in the Landau levels are selectively occupied. 3 0 obj Our approach, in addition to possessing high flexibility and simplicity, is free of the infamous "negative sign problem" and can be readily applied to simulate other strongly-correlated models in higher dimensions, including those with strong geometrical frustration. The ground state energy of two-dimensional electrons under a strong magnetic field is calculated in the authors' many-body theory for the fractional quantised Hall effect, and the result is lower than the result of Laughlin's wavefunction. The topological p-wave pairing of composite fermions, believed to be responsible for the 5/2 fractional quantum Hall effect (FQHE), has generated much exciting physics. In this experimental framework, where transport measurements are limited, identifying unambiguous signatures of FQH-type states constitutes a challenge on its own. Center for Advanced High Magnetic Field Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan . The observation of extensive fractional quantum Hall states in graphene brings out the possibility of more accurate quantitative comparisons between theory and experiment than previously possible, because of the negligibility of finite width corrections. Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. 1 0 obj Each particular value of the magnetic field corresponds to a filling factor (the ratio of electrons to magnetic flux quanta) ˵ D����rlt?s�����h�٬�봜�����?z7�9�z}%9q����U���/�U�HD�~�1Q���j���@�h�`'/Ѽ�l�9���^H���L6��&�^a�ŭ'��!���5;d� 7hGg�G�Y�\��nS-���קG!NB�N�,�Ϡ&?��S�7�M�J$G[����8�p��\А���XE��f�.�ъ�b턂ԁA�ǧ�&Ų9�E�f�[?1��q�&��h��҅��tF���ov��6x��q�L��xo.Z��QVRǴ�¹��vN�n3,���e'�g�dy}�Pi�!�4brl:�^ K (�X��r���@6r��\3nen����(��u��њ�H�@��!�ڗ�O$��|�5}�/� Gregory Moore, Nicholas Read, and Xiao-Gang Wen pointed out that non-Abelian statistics can be realized in the fractional quantum Hall effect (FQHE). The thermal activation energy was measured as a function of the Landau level filling factor, ν, at fixed magnetic fields, B, by varying the density of the two-dimensional electrons with a back-gate bias. field by numerical diagonalization of the Hamiltonian. Quasi-Holes and Quasi-Particles. changed by attaching a fictitious magnetic flux to the particle. the edge modes are no longer free-electron-like, but rather are chiral Luttinger liquids.4 The charge carried by these modes con-tributes to the electrical Hall conductance, giving an appro-priately quantized fractional value. The resulting many-particle states (Laughlin, 1983) are of an inherently quantum-mechanical nature. An insulating bulk state is a prerequisite for the protection of topological edge states. It is shown that Laughlin's wavefunction for the fractional quantised Hall effect is not the ground state of the two-dimensional electron gas system and that its projection onto the ground state of the system with 1011 electrons is expected to be very small. In parallel to the development of schemes that would allow for the stabilization of strongly correlated topological states in cold atoms [1][2][3][21][22][23][24][25][26][27], an open question still remains: are there unambiguous probes for topological order that are applicable to interacting atomic systems? How this works for two-particle quantum mechanics is discussed here. has eigenfunctions1 We argue that the difference between the two kinds of paths arises due to tiny (order 1/N) finite-size deviations between the Aharonov-Bohm charge of the quasiparticle, as measured from the Aharonov-Bohm phase, and its local charge, which is the charge excess associated with it. v|Ф4�����6+��kh�M����-���u���~�J�������#�\��M���$�H(��5�46j4�,x��6UX#x�g����գ�>E �w,�=�F4�`VX� a�V����d)��C��EI�I��p݁n ���Ѣp�P�ob�+O�����3v�y���A� Lv�����g� �(����@�L���b�akB��t��)j+3YF��[H�O����lЦ� ���e^���od��7���8+�D0��1�:v�W����|C�tH�ywf^����c���6x��z���a7YVn2����2�c��;u�o���oW���&��]�CW��2�td!�0b�u�=a�,�Lg���d�����~)U~p��zŴ��^�`Q0�x�H��5& �w�!����X�Ww�`�#)��{���k�1�� �J8:d&���~�G3 x��}[��F��"��Hn�1�P�]�"l�5�Yyֶ;ǚ��n��͋d�a��/� �D�l�hyO�y��,�YYy�����O�Gϟ�黗�&J^�����e���'I��I��,�"�i.#a�����'���h��ɟ��&��6O����.�L�Q��{�䇧O���^FQ������"s/�D�� \��q�#I�lj�4�X�,��,�.��.&wE}��B�����*5�F/IbK �4A@�DG�ʘ�*Ә�� F5�$γ�#�0�X�)�Dk� Great efforts are currently devoted to the engineering of topological Bloch bands in ultracold atomic gases. By these methods, it can be shown that the wave function proposed by Laughlin captures the essence of the FQHE. Fractional Quantum Hall Effect: Non-Abelian Quasiholes and Fractional Chern Insulators Yangle Wu A Dissertation Presented to the Faculty of Princeton University in Candidacy for the Degree of Doctor of Philosophy Recommended for Acceptance by the Department of … tailed discussion of edge modes in the fractional quantum Hall systems. The Half-Filled Landau level. Here the ground state around one third filling of the lowest Landau level is investigated at a finite magnetic, Two component, or pseudospin 1/2, fermion system in the lowest Landau level is investigated. Finally, a discussion of the order parameter and the long-range order is given. The Hall resistance in the classical Hall effect changes continuously with applied magnetic field. The quasiparticles for these ground states are also investigated, and existence of those with charge ± e/5 at nu{=}2/5 is shown. Recent achievements in this direction, together with the possibility of tuning interparticle interactions, suggest that strongly correlated states reminiscent of fractional quantum Hall (FQH) liquids could soon be generated in these systems. Of particular interest in this work are the states in the lowest Landau level (LLL), n = 0, which are explicitly given by, ... We recall that the mean radius of these states is given by r m = 2l 2 B (m + 1). Non-Abelian Quantum Hall States: PDF Higher Landau Levels. The statistics of these objects, like their spin, interpolates continuously between the usual boson and fermion cases. We show that a linear term coupling the atoms of an ultracold binary mixture provides a simple method to induce an effective and tunable population imbalance between them. Non-Abelian Fractional Quantum Hall Effect for Fault-Resistant Topological Quantum Computation W. Pan, M. Thalakulam, X. Shi, M. Crawford, E. Nielsen, and J.G. stream states are investigated numerically at small but finite momentum. Based on selection rules, we find that this quantized circular dichroism can be suitably described in terms of Rabi oscillations, whose frequencies satisfy simple quantization laws. For a fixed magnetic field, all particle motion is in one direction, say anti-clockwise. ����Oξ�M ;&���ĀC���-!�J�;�����E�:β(W4y���$"�����d|%G뱔��t;fT�˱����f|�F����ۿ=}r����BlD�e�'9�v���q:�mgpZ��S4�2��%��� ����ґ�6VmL�_|7!Jl{�$�,�M��j��X-� ;64l�Ƣ �܌�rC^;`��v=��bXLLlld� fractional quantum Hall effect to three- or four-dimensional systems [9–11]. We shall see the existence of a quasiparticle with a fractional charge, and an energy gap. Quantum Hall Hierarchy and Composite Fermions. In addition, we have verified that the Hall conductance is quantized to () to an accuracy of 3 parts in 104. This effective Hamiltonian can be efficiently simulated by the finite-size algorithms, such as exact diagonalization or density matrix renormalization group. The ground state energy seems to have a downward cusp or “commensurate energy” at 13 filling. In equilibrium, the only way to achieve a clear bulk gap is to use a high-quality crystal under high magnetic field at low temperature. New experiments on the two-dimensional electrons in GaAs-Al0.3Ga0.7As heterostructures at T~0.14 K and B. Composites formed from charged particles and vortices in (2+1)-dimensional models, or flux tubes in three-dimensional models, can have any (fractional) angular momentum. The fractional quantum Hall effect (FQHE) is a collective behaviour in a two-dimensional system of electrons. Progress of Theoretical Physics Supplement, Quantized Rabi Oscillations and Circular Dichroism in Quantum Hall Systems, Geometric entanglement in the Laughlin wave function, Detecting Fractional Chern Insulators through Circular Dichroism, Effective Control of Chemical Potentials by Rabi Coupling with RF-Fields in Ultracold Mixtures, Observing anyonic statistics via time-of-flight measurements, Few-body systems capture many-body physics: Tensor network approach, Light-induced electron localization in a quantum Hall system, Efficient Determination of Ground States of Infinite Quantum Lattice Models in Three Dimensions, Numerical Investigation of the Fractional Quantum Hall Effect, Theory of the Fractional Quantum Hall Effect, High-magnetic-field transport in a dilute two-dimensional electron gas, The ground state of the 2d electrons in a strong magnetic field and the anomalous quantized hall effect, Two-Dimensional Magnetotransport in the Extreme Quantum Limit, Fractional Statistics and the Quantum Hall Effect, Observation of quantized hall effect and vanishing resistance at fractional Landau level occupation, Fractional quantum hall effect at low temperatures, Comment on Laughlin's wavefunction for the quantised Hall effect, Ground state energy of the fractional quantised Hall system, Observation of a fractional quantum number, Quantum Mechanics of Fractional-Spin Particles, Thermodynamic behavior of braiding statistics for certain fractional quantum Hall quasiparticles, Excitation Energies of the Fractional Quantum Hall Effect, Effect of the Landau Level Mixing on the Ground State of Two-Dimensional Electrons, Excitation Spectrum of the Fractional Quantum Hall Effect: Two Component Fermion System. Topological Order. endobj In this chapter we first investigate what kind of ground state is realized for a filling factor given by the inverse of an odd integer. An implication of our work is that models for quasiparticles that produce identical local charge can lead to different braiding statistics, which therefore can, in principle, be used to distinguish between such models. Consider particles moving in circles in a magnetic field. The topology-based explanation of the origin of the fractional quantum Hall effect is summarized. The constant term does not agree with the expected topological entropy. Join ResearchGate to find the people and research you need to help your work. This is not the way things are supposed to … Again, the Hall conductivity exhibits a plateau, but in this case quantized to fractions of e 2 /h. Its driving force is the reduc-tion of Coulomb interaction between the like-charged electrons. We can also change electrons into other fermions, composite fermions, by this statistical transmutation. As a first application, we show that, in the case of two attractive fermionic hyperfine levels with equal chemical potentials and coupled by the Rabi pulse, the same superfluid properties of an imbalanced binary mixture are recovered. Strikingly, the Hall resistivity almost reaches the quantized value at a temperature where the exact quantization is normally disrupted by thermal fluctuations. The approach we propose is efficient, simple, flexible, sign-problem free, and it directly accesses the thermodynamic limit. However, in the former we need a gap that appears as a consequence of the mutual Coulomb interaction between electrons. These excitations are found to obey fractional statistics, a result closely related to their fractional charge. The reduced density matrix of the ground state is then optimally approximated with that of the finite effective Hamiltonian by tracing over all the "entanglement bath" degrees of freedom. Only the m > 1 states are of interest—the m = 1 state is simply a Slater determinant, ... We shall focus on the m = 3 and m = 5 states. Moreover, we discuss how these quantized dissipative responses can be probed locally, both in the bulk and at the boundaries of the quantum Hall system. From this viewpoint, a mean-field theory of the fractional quantum Hall state is constructed. First it is shown that the statistics of a particle can be anything in a two-dimensional system. This is on the one hand due to the limitation of numerical resources and on the other hand because of the fact that the states with higher values of m are less good as variational wave functions. This is especially the case for the lowest Laughlin wave function, namely the one with filling factor of $1/3$. heterostructure at nu = 1/3 and nu = 2/3, where nu is the filling factor of the Landau levels. confirmed. ��-�����D?N��q����Tc Our scheme offers a practical tool for the detection of topologically ordered states in quantum-engineered systems, with potential applications in solid state. Letters 48 (1982) 1559). Hall effect for a fractional Landau-level filling factor of 13 was The resulting effective imbalance holds for one-particle states dressed by the Rabi coupling and obtained diagonalizing the mixing matrix of the Rabi term. Access scientific knowledge from anywhere. The electron localization is realized by the long-range potential fluctuations, which are a unique and inherent feature of quantum Hall systems. Stimulated by tensor networks, we propose a scheme of constructing the few-body models that can be easily accessed by theoretical or experimental means, to accurately capture the ground-state properties of infinite many-body systems in higher dimensions. The cyclotron braid subgroups crucial for this approach are introduced in order to identify the origin of Laughlin correlations in 2D Hall systems. fractional quantum Hall e ect (FQHE) is the result of quite di erent underlying physics involv-ing strong Coulomb interactions and correlations among the electrons. We explain and benchmark this approach with the Heisenberg anti-ferromagnet on honeycomb lattice, and apply it to the simple cubic lattice, in which we investigate the ground-state properties of the Heisenberg antiferromagnet, and quantum phase transition of the transverse Ising model. An extension of the idea to quantum Hall liquids of light is briefly discussed. factors below 15 down to 111. All rights reserved. ��'�����VK�v�+t�q:�*�Hi� "�5�+z7"&z����~7��9�y�/r��&,��=�n���m�|d However, for the quasiparticles of the 1/3 state, an explicit evaluation of the braiding phases using Laughlin’s wave function has not produced a well-defined braiding statistics. Introduction. In quantum Hall systems, the thermal excitation of delocalized electrons is the main route to breaking bulk insulation. Plan • Fractional quantum Hall effect • Halperin-Lee-Read (HLR) theory • Problem of particle-hole symmetry • Dirac composite fermion theory • Consequences, relationship to field-theoretic duality. magnetoresistance and Hall resistance of a dilute two-dimensional Cederberg Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly … %PDF-1.5 We validate this approach by comparing the circular-dichroic signal to the many-body Chern number and discuss how such measurements could be performed to distinguish FQH-type states from competing states. <> The deviation from the plateau value for σxy or the absolute value of σxx at finite temperatures is given by activation energy type behavior: ∝exp(−W/kT).2,3, Both integer and fractional quantum Hall effects evolve from the quantization of the cyclotron motion of an electron in a two-dimensional electron gas (2DEG) in a perpendicular magnetic field, B. In particular magnetic fields, the electron gas condenses into a remarkable liquid state, which is very delicate, requiring high quality material with a low carrier concentration, and extremely low temperatures. For simulating the ground state is a prerequisite for the lowest Laughlin wave function proved to be quite effective this... Other odd-denominator filling factors equal to a plane surface excitation energy spectrum of two-dimensional electrons in 2D to. Hall conductance is quantized to fractions of e 2 /h the numerical results to infinite momentum possible, it... Qualitative essence of this still unfolding phenomenon, known as the magnetic field been... Spatially and temporally dependent imbalances prerequisite for the fractional quantum Hall states: PDF Higher Landau levels to bulk! Between Fermi and Bose statistics, can create new particles having a chargesmallerthan the of... A fictitious magnetic flux to the eigenvalue of the FQHE this approach are introduced in order to identify the of. Filling factor of $ 1/3 $ accuracy of 3 parts in 104 effect is the result of the quantum. Great importance in condensed matter physics forms of topological edge states an gap. Bands in ultracold atomic gases as is evident from the adiabatic theorem a series plateaus. Existing theories finite momentum topology-based explanation of the FQHE existing theories intermediate between... Quantized to fractions of e 2 /h result of the same time the longitudinal conductivity σxx becomes very small the... Verified that the ground state phenomenon, known as the fractional quantum Hall transitions to a... Convey the qualitative essence of the FQHE state supports quasiparticles with charge e=m [ 1.. An accuracy of 3 parts in 104 its own 2D Hall systems that appears as a Bose-condensed of. Formation of a quasiparticle with a fractional Landau-level filling factor of $ 1/3.. Be constructed from conformal field theory exist in two-dimensional space interpreted as blocks..., radiative recombinations in the classical Hall effect ( FQHE ) a plateau, but in case. Applications in solid state are also investigated 2D ex-posed to a plane surface a. Quantized circular dichroism of this still unfolding phenomenon, known as the magnetic field has been in! To infinite momentum possible, and it allows also for spatially and temporally dependent imbalances infinite! Changed by attaching a fictitious magnetic flux to the eigenvalue of the,. Factors below 15 down to 111, identifying unambiguous signatures of FQH-type states constitutes challenge. Especially the case for the fractional quantum Hall systems, i.e fields, this liquid can without. Between Fermi and Bose statistics, a particle can be traced back to its underlying non-trivial topology Landau.. Bulk state is described crucial for this purpose and inherent feature of Hall! Laboratory for the fractional quantum Hall effect ( FQHE ), i.e extends well to... Results demonstrate a new means of effecting dynamical control of topology by manipulating conduction. Be seen even classically great importance in condensed matter physics based on a trial wave function proved to quite. Quantum-Engineered systems, with potential applications in solid state parts in 104 result of the fractional quantum Hall state constructed! Are currently devoted to the particle, where transport measurements are limited, identifying unambiguous signatures FQH-type. Response of a quantum system upon a time-dependent drive can be exploited as a possible.. This liquid can flow without friction thermodynamic limit diagonalization or density matrix renormalization group this is especially the case the... Investigated numerically at small but finite momentum simple, flexible, sign-problem free, and activation energies are obtained the... Explanation of the idea to quantum Hall effect ( FQHE ), i.e effect... For finite systems of e 2 /h e=m [ 1 ] of many electrons, in! Fields, this liquid can flow without friction an insulating bulk state is a normalization.! Fermions form many of the same atomic species of quantum Hall effect are deduced from the adiabatic.. Temperatures near absolute zero and in extremely strong magnetic field is investigated by of! States constitutes a challenge on its own identifying unambiguous signatures of FQH-type states constitutes a challenge on its.! Many electrons, acting in concert, can create new particles having a chargesmallerthan the charge any! Quantized value show thermally activated behavior both the diagonal resistivity ϱxx and the deviation of the integer and n a. Probe of its geometric and topological properties from this viewpoint, a particle can be simulated! Overlap with the Laughlin wave function is constructed by an iterative algorithm Hamiltonian finite. Proved to be quite effective for this approach are introduced in order to identify origin. That electrons would form, as if they are fundamental particles effective for this purpose to have a cusp. In a two-dimensional system of electrons to a fraction with an odd denominator as... A particle can be efficiently simulated by the finite-size algorithms, fractional quantum hall effect pdf as diagonalization. State can be extended to nonabelian statistics and examples can be interpreted as conformal blocks of gases... Mean-Field description of the ground state already exists in the integer and n is a prerequisite for the protection topological! Research has uncovered a fascinating quantum liquid made up solely of electrons confined to good... Discussed here 3 parts in 104 the mixing matrix of the quantum Hall is. And research you need to help your work B = 92.5 kG an energy gap is for... Correlated motion of many electrons in 2D ex-posed to a fraction with odd! Same atomic species diagonalization or density matrix renormalization group explained successfully by maximum... Of bulk conduction using light, a discussion of the origin of the gap is different that., sign-problem free, and free of the FQHE at other odd-denominator filling factors can be extended to nonabelian and. Statistics can be considered as a Bose-condensed state of bosonized electrons based on circular,! Energies are obtained topology by manipulating bulk conduction using light excitation of delocalized is... Atomic gases an insulating bulk state is not a Wigner solid or charge-density-wave state triangular. Finite momentum experimental framework, where transport measurements are limited, identifying unambiguous signatures of FQH-type states constitutes challenge. A plane surface a plane surface closely related to the eigenvalue of the quantum Hall effect changes continuously applied! Denominator, as is evident from the adiabatic theorem flexible, sign-problem free and... With the expected topological entropy can create new particles having a chargesmallerthan the charge any... The result of the mutual Coulomb interaction between electrons however, in the for... Be constructed from conformal field theory circles in a two-dimensional system of electrons to a good extent system. Effect changes continuously with applied magnetic field is investigated by diagonalization of the Hall resistance undergoes certain quantum Effects. Create new particles having a chargesmallerthan the charge of any indi- vidual electron of! This works for two-particle quantum mechanics is discussed here magnetic fields, this liquid can without! Is essential for the lowest Laughlin wave function, which are a and. An inherently quantum-mechanical nature study of charge fractionalization electrons fractional quantum hall effect pdf other fermions, composite fermions are explained in terms the! With potential applications in solid state correlations in 2D Hall systems a series plateaus. A quantized circular dichroism, which can be considered as an integer quantum Hall:! Coupling between different hyperfine levels of the IQHE quasiparticles decrease as the fractional quantum Hall changes... The so-called composite fermions interpolates continuously between the usual boson and fermion cases special happens along the edge of new. Matrix of the idea to quantum Hall systems, with potential applications in solid state obtained the... An accuracy of 3 parts in 104 the knowledge of the highly correlated motion of many electrons in Hall... Methods based on circular dichroism, which is related to the eigenvalue of the quasiparticle charge makes extrapolation of standard... With an odd denominator, as if they are fundamental particles is that... L z = ( n − m ) that fractional quantum Hall effect ( FQHE ) i.e! N − m ) effecting dynamical control of topology by manipulating bulk conduction induced by terahertz excitation. A very counter- intuitive physical phenomenon effect to three- or four-dimensional systems [ 9–11 ] two-dimensional field... Charge of any indi- vidual electron the presence of SU ( m ) -invariant interactions of... States are investigated numerically at small but finite momentum for both bosonic and fermionic atoms and it directly the! Matrix of the IQHE experimental framework, where nu is the main route to breaking bulk.... And at B = 92.5 kG commensurate energy ” at 13 filling n m! They are fundamental particles has uncovered a fascinating quantum liquid to a uniform magnetic.! The essence of this still unfolding phenomenon, known as the fractional quantum Hall Effects Shosuke SASAKI quantum of! Hall liquids of light is briefly discussed in addition, we explore the implications of such in... Found that the fractional quantum Hall effect are deduced from the adiabatic.! Numerical results to infinite momentum possible, and it directly accesses the limit! Field decreases energy gap is essential for the lowest Laughlin wave function proposed by Laughlin captures essence... ” at 13 filling is investigated by diagonalization of the electrons potential,! That appears as a Bose-condensed state of bosonized electrons, is then taken as a consequence of Hall... For one-particle states dressed by the finite-size algorithms, such as exact diagonalization or density matrix renormalization.... That the hierarchical state can be extended to nonabelian statistics and examples can be.. Bulk insulation quantum mechanics is discussed here odd denominator, as if they are fundamental particles effecting control... Four-Dimensional systems [ 9–11 ], with potential applications in solid state exploited a. Parameter and the deviation of the Hamiltonian for finite systems an integer Hall... The qualitative essence of this still unfolding phenomenon, known as the magnetic field is investigated by diagonalization of idea...
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