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arXiv · 2409.09070

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

Tomasz Masłowski·Hadi Cheraghi·Jesko Sirker·Nicholas Sedlmayr
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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.

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Tomasz Masłowski, Hadi Cheraghi, Jesko Sirker, Nicholas Sedlmayr. 2024-09-07. Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models. https://doi.org/10.1103/physrevb.110.224302

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