The Slater determinant having the largest overlap with the Laughlin wave function is constructed by an iterative algorithm. 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. factors below 15 down to 111. a GaAs-GaAlAs heterojunction. %���� The magnetoresistance showed a substantial deviation from The ground state energy seems to have a downward cusp or “commensurate energy” at 13 filling. At the same time the longitudinal conductivity σxx becomes very small. This resonance-like dependence on ν is characterized by a maximum activation energy, Δm = 830 mK and at B = 92.5 kG. 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. • 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 . Download PDF Abstract: Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. © 2008-2021 ResearchGate GmbH. We propose a numeric approach for simulating the ground states of infinite quantum many-body lattice models in higher dimensions. 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. and eigenvalues This gap appears only for Landau-level filling factors equal to a fraction with an odd denominator, as is evident from the experimental results. linearity above 18 T and exhibited no additional features for filling We shall see the existence of a quasiparticle with a fractional charge, and an energy gap. M uch is understood about the frac-tiona l quantum H all effect. <>/XObject<>/Font<>/Pattern<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 2592 1728] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> 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 In this experimental framework, where transport measurements are limited, identifying unambiguous signatures of FQH-type states constitutes a challenge on its own. This effective Hamiltonian can be efficiently simulated by the finite-size algorithms, such as exact diagonalization or density matrix renormalization group. Each particular value of the magnetic field corresponds to a filling factor (the ratio of electrons to magnetic flux quanta) This work suggests alternative forms of topological probes in quantum systems based on circular dichroism. a quantum liquid to a crystalline state may take place. 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 Fractional Quantum Hall Effect: PDF Laughlin Wavefunctions, Plasma Analogy, Toy Hamiltonians. 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. 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. 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 … Numerical diagonalization of the Hamiltonian is done for a two dimensional system of up to six interacting electrons, in the lowest Landau level, in a rectangular box with periodic boundary conditions. Anyons, Fractional Charge and Fractional Statistics. $${\phi _{n,m}}(\overrightarrow r ) = \frac{{{e^{|Z{|^2}/4{l^2}}}}}{{\sqrt {2\pi } }}{G^{m,n}}(iZ/l)$$ (2) Preface . Introduction. It is shown that a filled Landau level exhibits a quantized circular dichroism, which can be traced back to its underlying non-trivial topology. 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. The resulting effective imbalance holds for one-particle states dressed by the Rabi coupling and obtained diagonalizing the mixing matrix of the Rabi term. An extension of the idea to quantum Hall liquids of light is briefly discussed. changed by attaching a fictitious magnetic flux to the particle. 3 0 obj Great efforts are currently devoted to the engineering of topological Bloch bands in ultracold atomic gases. It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. This is a peculiarity of two-dimensional space. The existence of an energy gap is essential for the fractional quantum Hall effect (FQHE). ˵ 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}�/� 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. The fractional quantum Hall e ect: Laughlin wave function The fractional QHE is evidently prima facie impossible to obtain within an independent-electron picture, since it would appear to require that the extended states be only partially occupied and this would immediately lead to a nonzero value of xx. 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. The fractional quantum Hall effect (FQHE) offers a unique laboratory for the experimental study of charge fractionalization. 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. Next, we consider changing the statistics of the electrons. Again, the Hall conductivity exhibits a plateau, but in this case quantized to fractions of e 2 /h. The ground state has a broken symmetry and no pinning. Quantum Hall Hierarchy and Composite Fermions. 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 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]. electron system with 6×1010 cm-2 carriers in This way of controlling the chemical potentials applies for both bosonic and fermionic atoms and it allows also for spatially and temporally dependent imbalances. 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". In addition, we have verified that the Hall conductance is quantized to () to an accuracy of 3 parts in 104. We finally discuss the properties of m-species mixtures in the presence of SU(m)-invariant interactions. 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. confirmed. fractional quantum Hall effect to be robust. About this book. Gregory Moore, Nicholas Read, and Xiao-Gang Wen pointed out that non-Abelian statistics can be realized in the fractional quantum Hall effect (FQHE). 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�! Letters 48 (1982) 1559). ��'�����VK�v�+t�q:�*�Hi� "�5�+z7"&z����~7��9�y�/r��&,��=�n���m�|d 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. Hall effect for a fractional Landau-level filling factor of 13 was This term is easily realized by a Rabi coupling between different hyperfine levels of the same atomic species. Here we report a transient suppression of bulk conduction induced by terahertz wave excitation between the Landau levels in a GaAs quantum Hall system. ., which is related to the eigenvalue of the angularmomentum operator, L z = (n − m) . These excitations are found to obey fractional statistics, a result closely related to their fractional charge. 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� $${\varepsilon _{n,m}} = \overline n {\omega _c}(n + \frac{1}{2})$$ (3). Here m is a positive odd integer and N is a normalization factor. <> The approach we propose is efficient, simple, flexible, sign-problem free, and it directly accesses the thermodynamic limit. 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. Center for Advanced High Magnetic Field Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan . The so-called composite fermions are explained in terms of the homotopy cyclotron braids. This is especially the case for the lowest Laughlin wave function, namely the one with filling factor of $1/3$. <> Theory of the Integer and Fractional Quantum Hall Effects Shosuke SASAKI . 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. 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. 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. How this works for two-particle quantum mechanics is discussed here. The quasiparticles for these ground states are also investigated, and existence of those with charge ± e/5 at nu{=}2/5 is shown. 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. 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. 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? endobj 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. 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. Excitation energies of quasiparticles decrease as the magnetic field decreases. 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. 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