Impurity-induced non-unitary criticality

TL;DR

This paper reveals how local non-Hermitian impurities in a (1+1)-dimensional free-fermion chain induce non-unitary conformal field theory criticality with central charge -2, connecting impurity physics with non-Hermitian quantum phenomena.

Contribution

It demonstrates that non-Hermitian impurities can drastically alter critical behavior, leading to non-unitary CFTs characterized by a central charge of -2, and explores their boundary condition sensitivity.

Findings

Identification of non-unitary CFT with c=-2 at impurity criticality

Sensitivity of non-unitary criticality to boundary conditions

Analysis of entanglement and spectrum scaling confirms non-Hermitian effects

Abstract

Quantum impurities give rise to rich physical phenomena, with some exhibiting critical behavior described by conformal field theories (CFTs) in the low-energy limit. In parallel, party-time ($\mathcal{PT}$) symmetric non-Hermitian systems host exceptional points (EPs) at criticality, leading to exotic features governed by non-unitary CFTs. Here, we establish a connection between non-Hermitian impurities and CFTs by demonstrating that the critical properties of a (1+1)-dimensional free-fermion chain with central charge $c=1$ can be drastically altered by the presence of a local non-Hermitian impurity. Through a systematic analysis of entanglement/R\'enyi entropy, the finite-size scaling of the many-body spectrum, and fidelity susceptibility, we identify that this impurity-induced non-Hermitian criticality is characterized by a non-unitary CFT with central charge $c=-2$. Furthermore, we find that these non-unitary critical properties exhibit strong sensitivity to boundary conditions.