Spectral line

Quantum mechanics

Theoretical physics

Ground state

Mathematical physics

Biology

Quantum spin Hall effect

Topological degeneracy

Degeneracy (biology)

Mathematical optimization

Hamiltonian (control theory)

Symmetry protected topological order

Physics

Topological order

Bioinformatics

Mathematics

Quantum

Combinatorics

Quantum Hall effect

Electron

Topology (electrical circuits)

Fractional quantum Hall effect

Quantum Zeno effect

Hermitian matrix

Quantum state

Open quantum system

Multiplet

Scientific Reports

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.

Non-Hermitian fractional quantum Hall states