Fate of non-Hermitian free fermions with Wannier-Stark ladder

TL;DR

This paper investigates how non-Hermitian free fermions with Wannier-Stark ladders exhibit unique entanglement behaviors and phases, revealing critical scaling and deviations from traditional localization theories.

Contribution

It introduces a detailed analysis of entanglement properties in non-Hermitian fermions with Wannier-Stark ladders, uncovering novel entanglement phases and critical behaviors.

Findings

Identification of two area law regions and an algebraic scaling region for entanglement entropy.

Observation of critical scaling behavior in finite-size systems.

Discovery of entanglement characteristics that differ from (1+1)d conformal field theory predictions.

Abstract

The Wannier-Stark localization dynamically alters the entanglement behavior of non-Hermitian free fermions. Utilizing the single-particle correlation matrix technique, we analyze the effective Hamiltonian of these fermions with a Wannier-Stark ladder. Under open boundary conditions, we observe the steady state half-chain entanglement entropy and identify two distinct area law regions and an algebraic scaling region. Finite-size scaling analysis reveals critical scaling behavior of the half-chain entanglement entropy. Notably, the system demonstrates unique entanglement characteristics under periodic boundary conditions, which diverge from the (1+1)d conformal field theory predictions for Anderson localization. Our findings highlight novel entanglement phases emerging from the interplay between the non-Hermitian skin effect and disorder-free localization.