Exploring Dynamical Quantum Phase Transitions via the Dynamical Phase Accumulated at an Equilibrium Critical Point
Abstract
We investigate dynamical quantum phase transitions (DQPTs) generated by a two-step linear quench with a finite waiting time at the equilibrium critical point. The waiting stage leads to the accumulation of a dynamical phase that depends on the waiting time and directly reflects the critical spectral structure. In the transverse Ising chain, this accumulated phase modifies the critical structure of DQPTs from a single-critical-mode (SCM) regime to a multiple-critical-mode (MCM) regime. We analytically and numerically determine the boundary between the two regimes. Along this boundary, the waiting time approaches a constant in the sudden-quench limit, whereas in the slow-quench limit it follows Kibble--Zurek (KZ) scaling with the quench time. In the SCM regime, the rate function exhibits a conventional linear singularity, r(t)−r(t*)∝ |t−t*|α, with the critical exponent α=1 near the critical time. At the SCM--MCM boundary, this exponent changes to α=1/2, leading to a divergent first derivative of the rate function. Additional discrete parameter lines with α=1/2 also appear within the MCM regime in the parameter plane spanned by the waiting and quench times. Our findings establish a direct connection between the accumulated dynamical phase and the critical structure of DQPTs, further supported by an extended Su--Schrieffer--Heeger (SSH) model.
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BibTeX
@misc{kou2026exploring,
title = {{Exploring Dynamical Quantum Phase Transitions via the Dynamical Phase Accumulated at an Equilibrium Critical Point}},
author = {Han-Chuan Kou and Peng Li and Zhi-Han Zhang and Zhen-Yu Zheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14591},
eprint = {2610.14591},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14591},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exploring Dynamical Quantum Phase Transitions via the Dynamical Phase Accumulated at an Equilibrium Critical Point
AU - Han-Chuan Kou
AU - Peng Li
AU - Zhi-Han Zhang
AU - Zhen-Yu Zheng
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14591
UR - https://arxiv.org/abs/2610.14591
AB - We investigate dynamical quantum phase transitions (DQPTs) generated by a two-step linear quench with a finite waiting time at the equilibrium critical point. The waiting stage leads to the accumulation of a dynamical phase that depends on the waiting time and directly reflects the critical spectral structure. In the transverse Ising chain, this accumulated phase modifies the critical structure of DQPTs from a single-critical-mode (SCM) regime to a multiple-critical-mode (MCM) regime. We analytically and numerically determine the boundary between the two regimes. Along this boundary, the waiting time approaches a constant in the sudden-quench limit, whereas in the slow-quench limit it follows Kibble--Zurek (KZ) scaling with the quench time. In the SCM regime, the rate function exhibits a conventional linear singularity, r(t)−r(t^*)∝ |t−t^*|^α, with the critical exponent α=1 near the critical time. At the SCM--MCM boundary, this exponent changes to α=1/2, leading to a divergent first derivative of the rate function. Additional discrete parameter lines with α=1/2 also appear within the MCM regime in the parameter plane spanned by the waiting and quench times. Our findings establish a direct connection between the accumulated dynamical phase and the critical structure of DQPTs, further supported by an extended Su--Schrieffer--Heeger (SSH) model.
ER -