Dynamic Phase Transitions in Periodically Driving 1D Ising Model

TL;DR

This paper explores how periodic driving induces dynamical quantum phase transitions in a 1D Ising model, revealing resonance conditions and frequency regimes that control the occurrence of these transitions.

Contribution

It demonstrates two distinct mechanisms for inducing DQPTs via periodic drives, including resonance within phases and crossing critical points, with detailed scaling relations.

Findings

Resonant drives trigger DQPTs within phases at specific frequencies.

Low-frequency drives induce DQPTs across phase boundaries.

High-frequency drives suppress DQPTs, inhibiting transitions.

Abstract

This work investigates dynamical quantum phase transitions (DQPTs) in a one-dimensional Ising model subjected to a periodically modulated transverse field. In contrast to sudden quenches, we demonstrate that DQPTs can be induced in two distinct ways. First, when the system remains within a given phase--ferromagnetic (FM) or paramagnetic (PM), a resonant periodic drive can trigger a DQPT when its frequency matches the energy-level transition of the system. The timescale for the transition is governed by the perturbation strength $\lambda'$, the critical mode $k_c$, and its energy gap $\Delta_{k_c}$, following the scaling relation $\tau \propto \sin^{-1}k_c \Delta_{k_c}\lambda'^{-1}$. Second, for drives across the critical point between the FM and PM phases, low frequencies can always induce DQPTs, regardless of resonance. This behavior stems from the degeneracy of the energy-level at the critical point, which ensures that any drive with a frequency lower than the system's intrinsic transition frequency will inevitably excite the system. However, in the high-frequency regime, such excitation will be strongly suppressed, thereby inhibiting the occurrence of DQPTs. This study provides deeper insight into the nonequilibrium dynamics of quantum spin chains.