Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916529360076800 |
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| author | Masłowski, Tomasz Cheraghi, Hadi Sirker, Jesko Sedlmayr, Nicholas |
| author_facet | Masłowski, Tomasz Cheraghi, Hadi Sirker, Jesko Sedlmayr, Nicholas |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_09070 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models Masłowski, Tomasz Cheraghi, Hadi Sirker, Jesko Sedlmayr, Nicholas Statistical Mechanics Mesoscale and Nanoscale Physics 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. |
| title | Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models |
| topic | Statistical Mechanics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2409.09070 |