Complex Berry phase and imperfect non-Hermitian phase transitions

TL;DR

This paper explores how complex Berry phases influence spectral phase transitions in non-Hermitian systems, revealing that cyclic adiabatic evolution can smooth these transitions due to the imaginary component of the Zak phase.

Contribution

It demonstrates that the imaginary part of the Zak phase causes imperfect spectral phase transitions in PT-symmetric non-Hermitian lattices under external fields.

Findings

Imperfect phase transitions are linked to a non-zero imaginary Zak phase.

Cyclic adiabatic evolution leads to smooth spectral transitions.

The study uses Wannier-Stark ladders in non-Hermitian lattices as a model.

Abstract

In many classical and quantum systems described by an effective non-Hermitian Hamiltonian, spectral phase transitions, from an entirely real energy spectrum to a complex spectrum, can be observed as a non-Hermitian parameter in the system is increased above a critical value. A paradigmatic example is provided by systems possessing parity-time (PT) symmetry, where the energy spectrum remains entirely real in the unbroken PT phase while a transition to complex energies is observed in the unbroken PT phase. Such spectral phase transitions are universally sharp. However, when the system is slowly and periodically cycled, the phase transition can become smooth, i.e. imperfect, owing to the complex Berry phase associated to the cyclic adiabatic evolution of the system. This remarkable phenomenon is illustrated by considering the spectral phase transition of the Wannier-Stark ladders in a PT-symmetric class of two-band non-Hermitian lattices subjected to an external dc field, unraveling that a non-vanishing imaginary part of the Zak phase -- the Berry phase picked up by a Bloch eigenstate evolving across the entire Brillouin zone -- is responsible for imperfect spectral phase transitions