Laughlin spin liquid states on lattices obtained from conformal field theory

Abstract

We propose a set of spin system wavefunctions that are very similar to lattice versions of the Laughlin states. The wavefunction are conformal blocks of conformal field theories, and for filling factor ν=1/2 we provide a parent Hamiltonian, which is valid for any even number of spins and is at the same time a 2D generalization of the Haldane-Shastry model. We also demonstrate that the Kalmeyer-Laughlin state is reproduced as a particular case of this model. Finally, we discuss various properties of the spin states and point out several analogies to known results for the Laughlin states.

5+6 pages, 4 figures

References in corpus (8)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement spectrum and boundary theories with projected entangled-pair states
• Entanglement entropy in fermionic Laughlin states
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Bipartite entanglement entropy in fractional quantum Hall states
• Topological Entanglement Entropy of Z2 Spin liquids and Lattice Laughlin states
• Topological Entanglement Entropy from the Holographic Partition Function
• Quantum spin Hamiltonians for the SU(2)_k WZW model

Cited by in corpus (83)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Spin liquid nature in the Heisenberg $J_1$-$J_2$ triangular antiferromagnet
• Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
• Realizing Fractional Chern Insulators with Dipolar Spins
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model
• Chiral Spin Liquid and Quantum Criticality in Extended $S=1/2$ Heisenberg Models on the Triangular Lattice
• Topological Flat Bands from Dipolar Spin Systems
• Momentum polarization: an entanglement measure of topological spin and chiral central charge
• Global phase diagram and quantum spin liquids in spin-1/2 triangular antiferromagnet
• Fractional quantum Hall states in lattices: Local models and physical implementation
• Microscopic models for Kitaev's sixteenfold way of anyon theories
• Coupled wire construction of chiral spin liquids
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• Nature of chiral spin liquids on the kagome lattice
• Scaling of the entanglement spectrum near quantum phase transitions
• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• Parent Hamiltonian for the non-Abelian chiral spin liquid
• Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice
• Chiral Spin Liquids in Arrays of Spin Chains
• Matrix Product States for Trial Quantum Hall States
• Topological models in rotationally symmetric quasicrystals
• Full counting statistics in the Haldane-Shastry chain
• Chiral spin liquids on the kagome Lattice
• Non-Abelian Fractional Chern Insulators from Long-Range Interactions
• Doping the chiral spin liquid -- topological superconductor or chiral metal?
• Lattice Laughlin States of Bosons and Fermions at Filling Fractions $1/q$
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Modular commutator in gapped quantum many-body systems
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model
• 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
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Infinite Matrix Product States for long range SU(N) spin models
• Quantum many-body scars with chiral topological order in 2D and critical properties in 1D
• Lattice effects on Laughlin wave functions and parent Hamiltonians
• Gapless chiral spin liquid from coupled chains on the kagome lattice
• Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model
• 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
• Chiral Spin Order in Kondo-Heisenberg systems
• Exact out-of-equilibrium central spin dynamics from integrability
• Continuum limit of lattice models with Laughlin-like ground states containing quasiholes
• Bosonic fractional quantum Hall states on the torus from conformal field theory
• Excited States in Spin Chains from Conformal Blocks
• Integrable open spin chains related to infinite matrix product states
• Majorana chiral spin liquid in Mott insulating cuprates
• Continuum limits of homogeneous binary trees and the Thompson group
• Possible SU(3) Chiral Spin Liquid on the Kagome Lattice
• Lattice Laughlin states on the torus from conformal field theory
• Optical lattice implementation scheme of a bosonic topological model with fermionic atoms
• Truncation of lattice fractional quantum Hall Hamiltonians derived from conformal field theory
• Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
• An analog of topological entanglement entropy for mixed states
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• Matrix product approximations to multipoint functions in two-dimensional conformal field theory
• Bosonic Gaussian states from conformal field theory
• Quantum state preparation of topological chiral spin liquids via Floquet engineering
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Edge states for the Kalmeyer-Laughlin wave function
• Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective
• Restricted Boltzmann machine representation for the groundstate and excited states of Kitaev Honeycomb model
• Adiabatic time evolution of highly excited states
• Matrix product approximations to conformal field theories
• A rapidly mixing Markov chain from any gapped quantum many-body system
• Field Tensor Network States
• Construction of spin models displaying quantum criticality from quantum field theory
• Simulating chiral spin liquids with projected entangled-pair states
• Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
• Conformal geometry from entanglement
• Quantum Thermal Hall effect of chiral spinons on a Kagome strip
• Many-body Lattice Wavefunctions From Conformal Blocks
• Chiral spin liquid phase in an optical lattice at mean-field level
• The BCS wave function, matrix product states, and the Ising conformal field theory
• Properties of Laughlin states on fractal lattices
• Effective description of correlations for states obtained from conformal field theory
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Approximate Hofstadter- and Kapit-Mueller-like parent Hamiltonians for Laughlin states on fractals
• Bulk-edge correspondence in the Haldane phase of the bilinear-biquadratic spin-1 Hamiltonian
• Chain and ladder models with two-body interactions and analytical ground states
• Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires