Kibble-Zurek scaling in the Yang-Lee edge singularity

TL;DR

This paper investigates the driven dynamics across Yang-Lee edge singularities in a finite quantum Ising chain, revealing that Kibble-Zurek scaling applies with critical exponents from different dimensional YLESes depending on system size.

Contribution

It demonstrates that Kibble-Zurek scaling describes the driven dynamics near YLES, with exponents varying by system size, extending understanding of non-Hermitian critical phenomena.

Findings

Kibble-Zurek scaling applies to small system sizes with 0+1D YLES exponents.

For medium sizes, two sets of critical exponents govern the dynamics.

Topological defect formation mechanism breaks down in YLES, yet scaling persists.

Abstract

We study the driven dynamics across the critical points of the Yang-Lee edge singularities (YLESes) in a finite-size quantum Ising chain with an imaginary symmetry-breaking field. In contrast to the conventional classical or quantum phase transitions, these phase transitions are induced by tuning the strength of the dissipation in a non-Hermitian system and can occur even at finite size. For conventional phase transitions, universal behaviors in driven dynamics across critical points are usually described by the Kibble-Zurek mechanism, which states that the scaling in dynamics is dictated by the critical exponents associated with one critical point and topological defects will emerge after the quench. While the mechanism leading to topological defects breaks down in the YLES, we find that for small lattice size, the driven dynamics can still be described by the Kibble-Zurek scaling with the exponents determined by the $(0+1)$-dimensional YLES. For medium finite size, however, the driven dynamics can be described by the Kibble-Zurek scaling with two sets of critical exponents determined by both the $(0+1)$-dimensional and the $(1+1)$-dimensional YLESes.