Fractional quantum Hall states in lattices: Local models and physical implementation

Abstract

The fractional quantum Hall (FQH) effect is one of the most striking phenomena in condensed matter physics. It is described by a simple Laughlin wavefunction and has been thoroughly studied both theoretically and experimentally. In lattice systems, however, such an effect has not been observed, there are few simple models displaying it, and only few mechanisms leading to it are known. Here we propose a new way of constructing lattice Hamiltonians with local interactions and FQH like ground states. In particular, we obtain a spin 1/2 model with a bosonic Laughlin like ground state, displaying a variety of topological features. We also demonstrate how such a model naturally emerges out of a Fermi-Hubbard like model at half filling, in which the kinetic energy part possesses bands with nonzero Chern number, and we show how this model can be implemented in an optical lattice setup with present technology.

7+5 pages, 5+1 figures, v2: references added

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Cited by in corpus (83)

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• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Projective symmetry group classification of chiral spin liquids
• Band structure engineering of ideal fractional Chern insulators
• Coupled wire construction of chiral spin liquids
• Tunable spin-spin interactions and entanglement of ions in separate wells
• Nature of chiral spin liquids on the kagome lattice
• Gapless chiral spin liquid in a kagome Heisenberg model
• Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice
• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid
• Chiral topological spin liquids with projected entangled pair states
• Chiral spin liquids on the kagome Lattice
• Enhanced thermal Hall effect in the square-lattice Néel state
• Emergence of Chiral Spin Liquids via Quantum Melting of Non-Coplanar Magnetic Orders
• Lattice Laughlin States of Bosons and Fermions at Filling Fractions $1/q$
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• SU(2)${}_1$ chiral edge modes of a critical spin liquid
• Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
• Lattice spin models for non-Abelian Chiral Spin Liquids
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Operation of a planar-electrode ion-trap array with adjustable RF electrodes
• Quantum cluster approach to the spinful Haldane-Hubbard model
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Bosonic Fractional Quantum Hall States on a Finite Cylinder
• Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons
• Abelian topological order of $\nu =2/5$ and $3/7$ fractional quantum Hall states in lattice models
• Lattice effects on Laughlin wave functions and parent Hamiltonians
• Time-dependent variational principle with controlled bond expansion for matrix product states
• Phonon Hall viscosity from phonon-spinon interactions
• Coherent generation of photonic fractional quantum Hall states in a cavity and the search for anyonic quasiparticles
• Topological Bootstrap: Fractionalization From Kondo Coupling
• Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model
• Chiral Topological Orders in an Optical Raman Lattice
• Wave Functions for Fractional Chern Insulators on Disk Geometry
• Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at $m=\frac{2}{3}$ magnetization
• Quantum phase diagram and chiral spin liquid in the extended spin-$\frac{1}{2}$ honeycomb XY model
• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
• Order by disorder in classical kagome antiferromagnets with chiral interactions
• Parent Hamiltonian Reconstruction of Jastrow-Gutzwiller Wavefunctions
• Chiral spin liquid and quantum phase diagram of spin-$1/2$ $J_1$-$J_2$-$J_{\chi }$ model on the square lattice
• Bosonic fractional quantum Hall states on the torus from conformal field theory
• Majorana chiral spin liquid in Mott insulating cuprates
• Excited States in Spin Chains from Conformal Blocks
• Spontaneous Chiral-Spin Ordering in Spin-Orbit Coupled Honeycomb Magnets
• Lattice Laughlin states on the torus from conformal field theory
• Possible SU(3) Chiral Spin Liquid on the Kagome Lattice
• Model wavefunctions for interfaces between lattice Laughlin states
• Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
• Truncation of lattice fractional quantum Hall Hamiltonians derived from conformal field theory
• Optical lattice implementation scheme of a bosonic topological model with fermionic atoms
• Fractional quantum Hall effect from frustration-free Hamiltonians
• Edge states for the Kalmeyer-Laughlin wave function
• Exact Topological Flat Bands from Continuum Landau Levels
• Bosonic Gaussian states from conformal field theory
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Quantum state preparation of topological chiral spin liquids via Floquet engineering
• Electronic States and Anomalous Hall Effect in Strongly Correlated Topological Systems
• Anomalous fractional quantum Hall effect and multi-valued Hamiltonians
• Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet
• Quantized thermal Hall conductance from edge current calculations in lattice models
• Frustrated quantum spin systems in small triangular lattices studied with a numerical method
• Simulating chiral spin liquids with projected entangled-pair states
• Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
• Many-body Lattice Wavefunctions From Conformal Blocks
• Variational Neural and Tensor Network Approximations of Thermal States
• Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
• Classical and quantum spin liquids
• Construction of spin models displaying quantum criticality from quantum field theory
• Interaction-driven transition between the Wigner crystal and the fractional Chern insulator in topological flat bands
• The BCS wave function, matrix product states, and the Ising conformal field theory
• Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States
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• Floquet dynamical chiral spin liquid at finite frequency
• Chiral Edge States Emerging on Anyon-Net
• Chiral Bosonic Topological Insulator on the Honeycomb Lattice with Anisotropic Interactions
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Exact Parent Hamiltonians for All Landau Level States in a Half-flux Lattice
• Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires