English

Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models

Statistical Mechanics 2024-12-19 v2 Mesoscale and Nanoscale Physics

Abstract

Dynamical quantum phase transitions are non-analyticities in a dynamical free energy (or return rate) which occur at critical times. Although extensively studied in one dimension, the exact nature of the non-analyticity in two and three dimensions has not yet been fully investigated. In two dimensions, results so far are known only for relatively simple two-band models. Here we study the general two- and three-dimensional cases. We establish the relation between the non-analyticities in different dimensions, and the functional form of the densities of Fisher zeroes. We show, in particular, that entering a critical region where the density of Fisher zeroes is non-zero at the boundary always leads to a cusp in the derivative of the return rate while the return rate itself is smooth. We illustrate our results by obtaining analytical results for exemplary two- and three-dimensional models.

Keywords

Cite

@article{arxiv.2409.09070,
  title  = {Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models},
  author = {Tomasz Masłowski and Hadi Cheraghi and Jesko Sirker and Nicholas Sedlmayr},
  journal= {arXiv preprint arXiv:2409.09070},
  year   = {2024}
}
R2 v1 2026-06-28T18:44:07.527Z