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.

5 pages, 3 figures, V2: changes in the presentation

References in corpus (3)

• Bose-Einstein condensation of chromium
• Putting competing orders in their place near the Mott transition
• Fractionalization, topological order, and quasiparticle statistics

Cited by in corpus (13)

• 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
• Emerging Bosons with Three-Body Interactions from Spin-1 Atoms in Optical Lattices
• Optical lattice quantum Hall effect
• Condensed Groundstates of Frustrated Bose-Hubbard Models
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• A real-space many-body marker for correlated ${\mathbb{Z}}_2$ topological insulators
• Growing quantum states with topological order
• Mott-Insulator Transition for Ultracold Fermions in Two-Dimensional Optical Lattices
• Chiral Gravitons on the Lattice
• Topological Phase Transitions of Interacting Fermions in the Presence of a Commensurate Magnetic Flux
• Hall-on-Toric: Descendant Laughlin state in the chiral ${\mathbb{Z}}_p$ toric code