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, $r(t)-r(t^{*})\propto |t-t^{*}|^\alpha$, with the critical exponent $\alpha=1$ near the critical time. At the SCM--MCM boundary, this exponent changes to $\alpha=1/2$, leading to a divergent first derivative of the rate function. Additional discrete parameter lines with $\alpha=1/2$ 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.

arXiv:2610.14591 [quant-ph]

(or arXiv:2610.14591v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.14591 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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