Metric-Changing Quasi-Hermitian Quenches: Normalized Loschmidt Amplitude and Complex-Time Zeros
Abstract
In quasi-Hermitian mixed-state quenches, the initial and final Hamiltonians generally possess different positive-definite metrics, so post-quench evolution is not quasi-unitary in the initial physical space. Choosing the preparation/measurement space as reference, we derive from first principles a normalized mixed-state Loschmidt amplitude using metric-compatible purifications. The resulting biorthogonal trace representation contains a normalization factor given by the norm of the evolved purification in the initial metric; this factor is essential for comparing states from different physical Hilbert spaces and directly encodes the metric mismatch. We prove that this normalization function is strictly positive on the real-time axis, so real-time criticality arises solely from destructive interference in the dynamical overlap. In complex time, zeros of the normalization factor generate branch singularities distinct from Fisher zeros. For a general two-level system, we derive analytic expressions for the Fisher and normalization zeros and analyze exceptional-point scaling together with the temperature- and quasi-Hermiticity-dependent DQPT critical times in two solvable quench protocols. In contrast to metric-stationary quenches, where non-Hermitian effects may be absorbed into an equivalent Hermitian description, the metric mismatch here produces genuine non-Hermitian dynamics: a time-dependent normalization factor and complex-time branch structure that cannot be removed by any global similarity transformation.
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BibTeX
@misc{hou2026metricchanging,
title = {{Metric-Changing Quasi-Hermitian Quenches: Normalized Loschmidt Amplitude and Complex-Time Zeros}},
author = {Xu-Yang Hou and Jia-Chen Tang and Hao Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20016},
eprint = {2610.20016},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20016},
}
RIS
TY - UNPB
TI - Metric-Changing Quasi-Hermitian Quenches: Normalized Loschmidt Amplitude and Complex-Time Zeros
AU - Xu-Yang Hou
AU - Jia-Chen Tang
AU - Hao Guo
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20016
UR - https://arxiv.org/abs/2610.20016
AB - In quasi-Hermitian mixed-state quenches, the initial and final Hamiltonians generally possess different positive-definite metrics, so post-quench evolution is not quasi-unitary in the initial physical space. Choosing the preparation/measurement space as reference, we derive from first principles a normalized mixed-state Loschmidt amplitude using metric-compatible purifications. The resulting biorthogonal trace representation contains a normalization factor given by the norm of the evolved purification in the initial metric; this factor is essential for comparing states from different physical Hilbert spaces and directly encodes the metric mismatch. We prove that this normalization function is strictly positive on the real-time axis, so real-time criticality arises solely from destructive interference in the dynamical overlap. In complex time, zeros of the normalization factor generate branch singularities distinct from Fisher zeros. For a general two-level system, we derive analytic expressions for the Fisher and normalization zeros and analyze exceptional-point scaling together with the temperature- and quasi-Hermiticity-dependent DQPT critical times in two solvable quench protocols. In contrast to metric-stationary quenches, where non-Hermitian effects may be absorbed into an equivalent Hermitian description, the metric mismatch here produces genuine non-Hermitian dynamics: a time-dependent normalization factor and complex-time branch structure that cannot be removed by any global similarity transformation.
ER -