Walking behavior induced by $\mathcal{PT}$ symmetry breaking in a non-Hermitian $\rm XY$ model with clock anisotropy

TL;DR

This paper investigates how breaking $ ext{PT}$ symmetry in a non-Hermitian XY model leads to unconventional phase transition behavior characterized by walking dynamics and pseudocriticality, contrasting with the $ ext{PT}$-symmetric case.

Contribution

It reveals that $ ext{PT}$ symmetry breaking induces a collision of fixed points resulting in walking behavior and pseudocriticality in a non-Hermitian XY model with clock anisotropy.

Findings

Unconventional scaling behavior emerges in the $ ext{PT}$ broken regime.

Correlation length exponent $ u=3/8$ in 2+1 dimensions.

Contrasts with $ ext{PT}$-symmetric case with multiple fixed points.

Abstract

A quantum system governed by a non-Hermitian Hamiltonian may exhibit zero temperature phase transitions that are driven by interactions, just as its Hermitian counterpart, raising the fundamental question how non-Hermiticity affects quantum criticality. In this context we consider a non-Hermitian system consisting of an $\rm XY$ model with a complex-valued four-state clock interaction that may or may not have parity-time-reversal ($\mathcal{PT}$) symmetry. When the $\mathcal{PT}$ symmetry is broken, and time-evolution becomes non-unitary, a scaling behavior similar to the Berezinskii-Kosterlitz-Thouless phase transition ensues, but in a highly unconventional way, as the line of fixed points is absent. From the analysis of the $d$-dimensional RG equations, we obtain that the unconventional behavior in the $\mathcal{PT}$ broken regime follows from the collision of two fixed points in the $d\to 2$ limit, leading to walking behavior or pseudocriticality. For $d=2+1$ the near critical behavior is characterized by a correlation length exponent $\nu=3/8$, a value smaller than the mean-field one. These results are in sharp contrast with the $\mathcal{PT}$-symmetric case where only one fixed point arises for $2<d<4$ and in $d=1+1$ three lines of fixed points occur with a continuously varying critical exponent $\nu$.