# Non-Hermitian fractional quantum Hall states

## TL;DR

This paper demonstrates the emergence of a non-Hermitian fractional quantum Hall state in systems with dissipation, revealing topological order and degeneracy without repulsive interactions, relevant to cold atom experiments.

## Contribution

It introduces a non-Hermitian FQH state driven by two-body interactions and dissipation, highlighting topological degeneracy and many-body Chern number in such systems.

## Key findings

- Topological degeneracy persists against non-Hermiticity.
- Non-Hermitian FQH state appears without repulsive interactions.
- Many-body Chern number indicates non-trivial topology.

## Abstract

We demonstrate the emergence of a topological ordered phase for non-Hermitian systems. Specifically, we elucidate that systems with non-Hermitian two-body interactions show a fractional quantum Hall (FQH) state. The non-Hermitian Hamiltonian is considered to be relevant to cold atoms with dissipation. We conclude the emergence of the non-Hermitian FQH state by the presence of the topological degeneracy and by the many-body Chern number for the ground state multiplet showing $C_{\mathrm{tot}}=1$. The robust topological degeneracy against non-Hermiticity arises from the many-body translational symmetry. Furthermore, we discover that the FQH state emerges without any repulsive interactions, which is attributed to a phenomenon reminiscent of the continuous quantum Zeno effect.