Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model

Abstract

An important class of model Hamiltonians for investigation of topological phases of matter consists of mobile, interacting particles on a lattice subject to a semi-classical gauge field, as exemplified by the bosonic Harper-Hofstadter model. A unique method for investigations of two-dimensional quantum systems are the infinite projected-entangled pair states (iPEPS), as they avoid spurious finite size effects that can alter the phase structure. However, due to no-go theorems in related cases this was often conjectured to be impossible in the past. In this letter, we show that upon variational optimization the infinite projected-entangled pair states can be used to this end, by identifying fractional Hall states in the bosonic Harper-Hofstadter model. The obtained states are characterized by showing exponential decay of bulk correlations, as dictated by a bulk gap, as well as chiral edge modes via the entanglement spectrum.

References in corpus (22)

• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Fractional Quantum Hall Effect in Optical Lattices
• Characterizing topological order by studying the ground states of an infinite cylinder
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Realization of a fractional quantum Hall state with ultracold atoms
• Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians
• Emerging Bosons with Three-Body Interactions from Spin-1 Atoms in Optical Lattices
• Pair-density-wave and chiral superconductivity in twisted bilayer transition-metal-dichalcogenides
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Bosonic Fractional Quantum Hall States on a Finite Cylinder
• Bosonic Pfaffian State in the Hofstadter-Bose-Hubbard Model
• Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Chiral spin liquids on the kagome lattice with projected entangled simplex states
• Generating function for projected entangled-pair states
• Symmetric projected entangled-pair states analysis of a phase transition in coupled spin-1/2 ladders

Cited by in corpus (12)

• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
• Accurate neural quantum states for interacting lattice bosons
• Spectral functions with infinite projected entangled-pair states
• Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
• Approximately-symmetric neural networks for quantum spin liquids
• Quantum spin liquid phase in the Shastry-Sutherland model revealed by high-precision infinite projected entangled-pair states
• Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States
• Accelerating two-dimensional tensor network contractions using QR decompositions
• Hall-on-Toric: Descendant Laughlin state in the chiral ${\mathbb{Z}}_p$ toric code
• Variational optimization of projected entangled-pair states on the triangular lattice
• Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires
• Accurate computation of the energy variance and $⟨⟨{\mathcal{L}}^{†}\mathcal{L}⟩⟩$ using iPEPS