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