Characterization of topological states on a lattice with Chern number

TL;DR

This paper uses Chern numbers to numerically identify topological order in strongly interacting lattice systems, especially bosonic fractional quantum Hall states, where traditional methods fail due to lattice effects.

Contribution

It introduces a Chern number-based approach for characterizing topological states on lattices, overcoming limitations of overlap calculations with continuum models.

Findings

Chern numbers successfully identify topological order in lattice FQH states.

The method distinguishes topological phases despite lattice-induced deviations.

It provides a numerical tool for studying strongly correlated topological systems.

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.