Spectral flow of non-hermitian Heisenberg spin chain with complex twist

TL;DR

This paper studies how the energy spectrum of a non-hermitian Heisenberg spin chain changes with complex boundary conditions, revealing a $4 o 8 o 12 o ext{etc.}$ periodicity transition linked to non-hermitian effects and metal-insulator transitions.

Contribution

It introduces the spectral flow behavior of a non-hermitian Heisenberg spin chain with complex twist, highlighting a novel periodicity jump phenomenon.

Findings

Spectral flow period is $4 extpi$ up to a critical imaginary twist.

Beyond the critical twist, the period increases successively.

The phenomenon is related to non-hermitian properties and metal-insulator transition.

Abstract

We investigate the spectral flow of the integrable non-hermitian Heisenberg spin chain under boundary conditions with complex twist angle. It is shown that the period of the spectral flow is $4\pi$ up to a certain critical imaginary twist, beyond which the period jumps successively to higher values. We argue that this phenomenon caused by non-hermitian properties of the system is closely related to the metal-insulator transition caused by non-hermitian hoppings for the one-dimensional insulator.