Logarithmic singularity in a dynamical quantum phase transition for free fermions
Abstract
We study the Loschmidt echo in a system of N non-interacting spinless lattice fermions released from a double-domain-wall initial state. In the large-N limit, the return probability is characterized by a large-deviation rate function known as the dynamical free energy. The Loschmidt echo is dominated by a complex instanton configuration, and the dynamical free energy develops a logarithmic singularity at the dynamical quantum phase transition. We obtain analytical results in the short-time and long-time regimes and support them with numerical computations. We show that the transition can be understood as a topological change of the dominant instanton configuration, analogous to the emergence of a cut in random matrix theory. We further show that post-selection can drive the system through two successive DQPTs, associated with successive topological changes of the dominant instanton configuration in complex time.
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BibTeX
@misc{bezzaz2026logarithmic,
title = {{Logarithmic singularity in a dynamical quantum phase transition for free fermions}},
author = {Yasser Bezzaz and Dimitri M Gangardt and Pavel L Krapivsky and Jean-Marc Luck and Kirone Mallick and Sylvain Prolhac},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18208},
eprint = {2609.18208},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05781697v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Logarithmic singularity in a dynamical quantum phase transition for free fermions
AU - Yasser Bezzaz
AU - Dimitri M Gangardt
AU - Pavel L Krapivsky
AU - Jean-Marc Luck
AU - Kirone Mallick
AU - Sylvain Prolhac
PY - 2026
DA - 2026/09/16
PB - HAL
DO - 10.48550/arxiv.2609.18208
UR - https://hal.science/hal-05781697v1
AB - We study the Loschmidt echo in a system of N non-interacting spinless lattice fermions released from a double-domain-wall initial state. In the large-N limit, the return probability is characterized by a large-deviation rate function known as the dynamical free energy. The Loschmidt echo is dominated by a complex instanton configuration, and the dynamical free energy develops a logarithmic singularity at the dynamical quantum phase transition. We obtain analytical results in the short-time and long-time regimes and support them with numerical computations. We show that the transition can be understood as a topological change of the dominant instanton configuration, analogous to the emergence of a cut in random matrix theory. We further show that post-selection can drive the system through two successive DQPTs, associated with successive topological changes of the dominant instanton configuration in complex time.
ER -