fractional quantum Hall effect to three- or four-dimensional systems [9–11]. The electron localization is realized by the long-range potential fluctuations, which are a unique and inherent feature of quantum Hall systems. We finally discuss the properties of m-species mixtures in the presence of SU(m)-invariant interactions. The formation of a Wigner solid or charge-density-wave state with triangular symmetry is suggested as a possible explanation. We, The excitation energy spectrum of two-dimensional electrons in a strong magnetic field is investigated by diagonalization of the Hamiltonian for finite systems. <> 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 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. 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). The Hall resistance in the classical Hall effect changes continuously with applied magnetic field. Rev. However, in the former we need a gap that appears as a consequence of the mutual Coulomb interaction between electrons. ���"��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�! The statistics of these objects, like their spin, interpolates continuously between the usual boson and fermion cases. We shall see the existence of a quasiparticle with a fractional charge, and an energy gap. All rights reserved. About this book. As in the integer quantum Hall effect, the Hall resistance undergoes certain quantum Hall transitions to form a series of plateaus. Our scheme offers a practical tool for the detection of topologically ordered states in quantum-engineered systems, with potential applications in solid state. 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. Again, the Hall conductivity exhibits a plateau, but in this case quantized to fractions of e 2 /h. Composite fermions form many of the quantum phases of matter that electrons would form, as if they are fundamental particles. field by numerical diagonalization of the Hamiltonian. has eigenfunctions1 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. We shall see that the fractional quantum Hall state can be considered as a Bose-condensed state of bosonized electrons. 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 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]. Quantum Hall Hierarchy and Composite Fermions. 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. stream The basic principle is to transform the Hamiltonian on an infinite lattice to an effective one of a finite-size cluster embedded in an "entanglement bath". ��'�����VK�v�+t�q:�*�Hi� "�5�+z7"&z����~7��9�y�/r��&,��=�n���m�|d ]����$�9Y��� ���C[�>�2RNJ{l5�S���w�o� This gap appears only for Landau-level filling factors equal to a fraction with an odd denominator, as is evident from the experimental results. The resulting effective imbalance holds for one-particle states dressed by the Rabi coupling and obtained diagonalizing the mixing matrix of the Rabi term. ����Oξ�M ;՘&���ĀC���-!�J�;�����E�:β(W4y���$"�����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� The fact that something special happens along the edge of a quantum Hall system can be seen even classically. This is especially the case for the lowest Laughlin wave function, namely the one with filling factor of $1/3$. 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. 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. The statistics of a particle can be. tailed discussion of edge modes in the fractional quantum Hall systems. Here m is a positive odd integer and N is a normalization factor. Great efforts are currently devoted to the engineering of topological Bloch bands in ultracold atomic gases. Access scientific knowledge from anywhere. However, in the case of the FQHE, the origin of the gap is different from that in the case of the IQHE. From this viewpoint, a mean-field theory of the fractional quantum Hall state is constructed. <>>> 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. 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