Kibble-Zurek dynamics across the first-order quantum transitions of quantum Ising chains in the thermodynamic limit

• URL: http://arxiv.org/abs/2507.00178v1
• Date: Mon, 30 Jun 2025 18:35:45 GMT
• Title: Kibble-Zurek dynamics across the first-order quantum transitions of quantum Ising chains in the thermodynamic limit
• Authors: Andrea Pelissetto, Davide Rossini, Ettore Vicari,
• Abstract summary: We study the out-of-equilibrium Kibble-Zurek dynamics in quantum Ising chains in a transverse field.<n>In finite-size systems, the KZ dynamics develops out-of-equilibrium finite-size scaling (OFSS) behaviors.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the out-of-equilibrium Kibble-Zurek (KZ) dynamics in quantum Ising chains in a transverse field, driven by a time-dependent longitudinal field $h(t)=t/t_s$ ($t_s$ is the time scale of the protocol), across their first-order quantum transitions (FOQTs) at $h=0$. The KZ protocol starts at time $t_i<0$ from the negatively magnetized ground state for $h_i = t_i/t_s<0$. Then, the system evolves unitarily up to a time $t_f > 0$, such that the magnetization of the state at time $t_f$ is positive. In finite-size systems, the KZ dynamics develops out-of-equilibrium finite-size scaling (OFSS) behaviors. Their scaling variables depend either exponentially or with a power law on the size, depending on the boundary conditions (BC). The OFSS functions can be computed in effective models restricted to appropriate low-energy (magnetized and/or kink) states. The KZ scaling behavior drastically changes in the thermodynamic limit (TL), defined as the infinite-size limit keeping $t$ and $t_s$ fixed, which appears substantially unrelated with the OFSS regime, because it involves higher-energy multi-kink states, which are irrelevant in the OFSS limit. The numerical analyses of the KZ dynamics in the TL show the emergence of a quantum spinodal-like scaling behavior at the FOQTs for all considered BC, which is independent of the BC. The longitudinal magnetization changes sign at $h(t)=h*>0$, where $h*$ decreases with increasing $t_s$, as $h*\sim 1/\ln t_s$. Moreover, in the large-$t_s$ limit, the time-dependence of the magnetization is described by a universal function of $\Omega = t/\tau_s$, with $\tau_s = t_s/\ln t_s$.

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