A note on topological insulator phase in non-hermitian quantum systems

TL;DR

This paper explores topological insulator phases in non-hermitian quantum systems across various dimensions, demonstrating real eigenvalues and invariants similar to hermitian systems, and proposes a classification scheme for these phases.

Contribution

It introduces a classification scheme for topological insulator phases in pseudo-hermitian quantum systems, linking non-hermitian Hamiltonians to hermitian counterparts via similarity transformations.

Findings

Non-hermitian Hamiltonians can have real bulk eigenvalues.

Topological invariants are preserved under similarity transformations.

A classification scheme for non-hermitian topological insulators is proposed.

Abstract

Examples of non-hermitian quantum systems admitting topological insulator phase are presented in one, two and three space dimensions. All of these non-hermitian Hamiltonians have entirely real bulk eigenvalues and unitarity is maintained with the introduction of appropriate inner-products in the corresponding Hilbert spaces. The topological invariant characterizing a particular phase is shown to be identical for a non-hermitian Hamiltonian and its hermitian counterpart, to which it is related through a non-unitary similarity transformation. A classification scheme for topological insulator phases in pseudo-hermitian quantum systems is suggested.