Characterization of topological states on a lattice with Chern number

Abstract

We study Chern numbers to characterize the ground state of strongly interacting systems on a lattice. This method allows us to perform a numerical characterization of bosonic fractional quantum Hall (FQH) states on a lattice where conventional overlap calculation with known continuum case such as Laughlin state, breaks down due to the lattice structure or dipole-dipole interaction. The non-vanishing Chern number indicates the existence of a topological order in the degenerate ground state manifold.

arXiv comment5 pages, 3 figures, V2: changes in the presentation

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Cited by in corpus (25)

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• Gauge fields for ultracold atoms in optical superlattices
• Ultracold atomic gases in non-Abelian gauge potentials: The case of constant Wilson loop
• Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy
• Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice
• Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks
• Emerging Bosons with Three-Body Interactions from Spin-1 Atoms in Optical Lattices
• Optical lattice quantum Hall effect
• Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice
• Condensed Groundstates of Frustrated Bose-Hubbard Models
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Three-level Haldane-like model on dice optical lattice
• The anisotropic Harper-Hofstadter-Mott model: competition between condensation and magnetic fields
• Optical Lattice with Torus Topology
• Vortex Dynamics and Hall Conductivity of Hard Core Bosons
• Vortex quantum dynamics of two dimensional lattice bosons
• A real-space many-body marker for correlated ${\mathbb{Z}}_2$ topological insulators
• Lattice Laughlin states on the torus from conformal field theory
• Measuring Berry curvature with quantum Monte Carlo
• Growing quantum states with topological order
• Mott-Insulator Transition for Ultracold Fermions in Two-Dimensional Optical Lattices
• Cold atoms in U(3) gauge potentials
• Chiral Gravitons on the Lattice
• Hall-on-Toric: Descendant Laughlin state in the chiral ${\mathbb{Z}}_p$ toric code
• Topological Phase Transitions of Interacting Fermions in the Presence of a Commensurate Magnetic Flux