Semi-localization transition driven by a single asymmetrical tunneling

TL;DR

This paper explores a novel quantum phase transition in a non-Hermitian system caused by a single asymmetrical impurity, leading to semi-localization with system-size decay length and non-analytic spectral statistics.

Contribution

It introduces the concept of semi-localization transition driven by a non-Hermitian impurity, revealing a new quantum phase with unique properties and symmetry-breaking effects.

Findings

Identification of semi-localization state with system-size decay length

Spectral statistics exhibit non-analytic behavior at transition

Ground state observables show second-order QPT characteristics

Abstract

A local impurity usually only strongly affects few single-particle energy levels, thus cannot induce a quantum phase transition (QPT), or any macroscopic quantum phenomena in a many-body system within the Hermitian regime. However, it may happen for a non-Hermitian impurity. We investigate the many-body ground state property of a one-dimensional tight-binding ring with an embedded single asymmetrical dimer based on exact solutions. We introduce the concept of semi-localization state to describe a new quantum phase, which is a crossover from extended to localized state. The peculiar feature is that the decay length is of the order of the system size, rather than fixed as a usual localized state. In addition, the spectral statistics is non-analytic as asymmetrical hopping strengths vary, resulting a sudden charge of the ground state. The distinguishing feature of such a QPT is that the density of ground state energy varies smoothly due to unbroken symmetry. However, there are other observables, such as the groundstate center of mass and average current, exhibit the behavior of second-order QPT. This behavior stems from time-reversal symmetry breaking of macroscopic number of single-particle eigen states.