We study the anisotropic effect of the Coulomb interaction on a 1/3-filling fractional quantum Hall system by using an exact diagonalization method on small systems in torus geometry. For weak anisotropy the system remains to be an incompressible quantum liquid, although anisotropy manifests itself in density correlation functions and excitation spectra. When the strength of anisotropy increases, we find the system develops a Hall-smectic-like phase with a one-dimensional charge density wave order and is unstable towards the one-dimensional crystal in the strong anisotropy limit. In all three phases of the Laughlin liquid, Hall-smectic-like, and crystal phases the ground state of the anisotropic Coulomb system can be well described by a family of model wave functions generated by an anisotropic projection Hamiltonian. We discuss the relevance of the results to the geometrical description of fractional quantum Hall states proposed by Haldane [ Phys. Rev. Lett. 107 116801 (2011)].
Viewpoint: Toward Fractional Quantum Hall physics with cold atoms
关于Nigel R. Cooper和Jean Dalibard，“利用光通量晶格达到分数量子霍尔态”，Phys.Rev.Lett。110，185301（2013）和N. Y. Yao、黄毛菊A. V. Gorshkov，C. R. Laumann，A. M. Läuchli，J. Ye，and M. D. Lukin，“Realizing Fractional Chern Insulators in Dipolar Spin Systems”，Phys. Rev. Lett. 110，185302（2013）。研究人员提出了使用超冷原子和分子重建分数量子霍尔物理学的新方法。
We formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field. Self-consistent solutions of the KS equations demonstrate that our formulation captures not only configurations with non-uniform densities but also topological properties such as fractional charge and fractional braid statistics for the quasiparticles excitations. This method should enable a realistic modeling of the edge structure, the effect of disorder, spin physics, …
Quantum Hall effects with multicomponent internal degrees of freedom facilitate the playground of novel emergent topological orders. Here, we explore the correlated topological phases of two-component hardcore bosons at a total filling factor $ν=2/5$ in both lattice Chern band models and Landau level continuum model under the interplay of intracomponent and intercomponent repulsions. We give the numerically theoretical demonstration of the emergence of two competing distinct fractional quantum Hall states: Halperin (441) fractional quantum Hall effect and Halperin (223) fractional quantum Hall…
We construct a class of lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be controllably solved in their low energy sectors, through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem and is generalizable.
Fractional quantum Hall-superconductor heterostructures may provide a platform towards non-abelian topological modes beyond Majoranas. However their quantitative theoretical study remains extremely challenging. We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. The fully gapped edges carry a topological degree of freedom that can encode quantum information protected against local perturbations. We simulate such a system numerically using exact diagonalization by restricting the calculation to the quasihole…
We develop a hydrodynamic field theory of the three-dimensional fractional quantum Hall effect, which was recently proposed to exist in magnetic Weyl semimetals, when the Weyl nodes are gapped by strong repulsive interactions. This theory takes the form of a BF theory, which contains both one-form and two-form gauge fields, coupling to quasiparticle and loop excitations correspondingly. It may be regarded as a generalization of the Chern-Simons theory of two-dimensional fractional quantum Hall liquids to three dimensions.
Incompressible even denominator fractional quantum Hall states at fillings $ν= \pm \frac{1}{2}$ and $ν= \pm \frac{1}{4}$ have been recently observed in monolayer graphene. We use a Chern-Simons description of multi-component fractional quantum Hall states in graphene to investigate the properties of these states and suggest variational wavefunctions that may describe them. We find that the experimentally observed even denominator fractions and standard odd fractions (such as $ν=1/3, 2/5$, etc.) can be accommodated within the same flux attachment scheme and argue that they may arise from sublat…
We derive the low-energy theory of semi-quantized quantum Hall states, a recently observed class of gapless bilayer fractional quantum Hall states. Our theory shows these states to feature gapless quasiparticles of fractional charge coupled to an emergent Chern-Simons gauge field. These gapless quasiparticles can be understood as composites of electrons and Laughlin-like quasiparticles. We show that semi-quantized quantum Hall states exhibit perfect interlayer drag, host non-Fermi liquid physics, and serve as versatile parent states for fully gapped topological phases hosting anyonic excitatio…
We elucidate the nature of neutral collective excitations of fractional quantum Hall liquids in the long-wavelength limit. We demonstrate that they are chiral gravitons carrying angular momentum - 2, which are quanta of quantum motion of an internal metric, and show up as resonance peaks in the systems response to what is the fractional Hall analog of gravitational waves. Relation with existing and possible future experimental work that can detect these fractional quantum Hall gravitons and reveal their chirality are discussed.
A fractionally quantized Berry phase is examined numerically in an anisotropic spin-1/2 XXZ model on the Kagome lattice. It is shown that the Berry phase has a fractionally quantized and non-zero value when an anisotropy is increased, which is consistent with the emergence of the tripartite entangled plaquette phase discussed by J. Carrasquilla et al. [Phys. Rev. B96, 054405 (2017)].
We discuss anomalous fractional quantum Hall effect that exists without external magnetic field. We propose that excitations in such systems may be described effectively by non-interacting particles with the Hamiltonians defined on the Brillouin zone with a branch cut. Hall conductivity of such a system is expressed through the one-particle Green function. We demonstrate that for the Hamiltonians of the proposed type this expression takes fractional values times Klitzing constant. Possible relation of the proposed construction with degeneracy of ground state is discussed as well.
We construct a class of 2+1 dimensional relativistic quantum field theories which exhibit the Fractional Quantum Hall Effect in the infrared, both in the continuum and on the lattice. The UV completion consists of a perturbative $U(1)\times U(1)$ gauge theory with only integer-charged fields, while the low energy spectrum consists of nontrivial topological phases supporting fractional currents, fractionally charged chiral surface modes and bulk anyonic excitations. Exotic phenomena such as a Fractional Quantum Spin Hall Effect can arise in such models.
We study $N$-component interacting particles (hardcore bosons and fermions) loaded in topological lattice models with SU$(N)$-invariant interactions based on density matrix renormalization group method. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that a class of SU$(N)$ fractional quantum Hall states can emerge at fractional filling factors $ν=N/(N+1)$ for bosons ($ν=N/(2N+1)$ for fermions) in the lowest Chern band, characterized by the nontrivial fractional Hall responses and the fractional charge pumping. Moreover, we establish a topological characte…
We study the time-dependent dynamical phase of fractional quasiparticles in quantum Hall states using Ramsey interferometry. A Ramsey two-pulse voltage modulation generates an interference term in the current noise of a quantum point contact oscillating with the dynamical phase. We show that the interference pattern probes the Green's function of the fractional quasi-particles in the time domain and reveals the fractional charge. We address both the case of a point-like tunnel junction and the case of momentum-resolved tunneling which also provides information on the speed of those quasipartic…
Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories
在适当的质量和Ω-背景参数下，利用N=2超共形规范规范理论的瞬子划分，确定了描述分数量子Hall系统中非阿贝尔统计的Moore-Read波函数.这是通过将最近由Alday-Gaiotto-Tachikawa发现的SU（2）规范场/刘维场论对偶推广到有理共形场论而得到的。指出了Moore-Read Hall $n$体波函数与Z_n等变Donaldson多项式之间的直接联系。
