# Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks

## TL;DR

This paper demonstrates, using tensor network methods, that the Harper-Hofstadter model with hard-core bosons on a lattice exhibits a topological fractional quantum Hall phase at filling factor 1/2, with robust properties and measurable topological invariants.

## Contribution

It provides the first tensor network evidence of a lattice fractional quantum Hall state in the interacting Hofstadter model, including topological entanglement entropy estimation.

## Key findings

- Supports the $
u=1/2$ fractional quantum Hall phase on the lattice.
- Measures the many-body Chern number confirming topological order.
- Shows gapless edge modes via Green function analysis.

## Abstract

We show via tensor network methods that the Harper-Hofstadter Hamiltonian for hard-core bosons on a square geometry supports a topological phase realizing the $\nu=1/2$ fractional quantum Hall effect on the lattice. We address the robustness of the ground state degeneracy and of the energy gap, measure the many-body Chern number, and characterize the system using Green functions, showing that they decay algebraically at the edges of open geometries, indicating the presence of gapless edge modes. Moreover, we estimate the topological entanglement entropy by taking a combination of lattice bipartitions that reproduces the topological structure of the original proposals by Kitaev and Preskill, and Levin and Wen. The numerical results show that the topological contribution is compatible with the expected value $\gamma = 1/2$. Our results provide extensive evidence that FQH states are within reach of state-of-the-art cold atom experiments.