Quantum quenches across continuous and first-order quantum transitions in one-dimensional quantum Ising models

TL;DR

This paper studies the out-of-equilibrium quantum dynamics in the one-dimensional quantum Ising model when parameters are suddenly changed across different types of quantum phase transitions, highlighting the effects of integrability and chaos.

Contribution

It provides a detailed analysis of quantum quenches crossing both continuous and first-order quantum transitions in the quantum Ising chain, including the impact of integrability breaking and chaos.

Findings

Distinct dynamical behaviors observed for quenches across different phases.

Chaotic regime emerges when the spectrum is nonintegrable, affecting thermalization.

Qualitative differences in dynamics depending on whether the quench crosses a CQT or FOQT.

Abstract

We investigate the quantum dynamics generated by quantum quenches (QQs) of the Hamiltonian parameters in many-body systems, focusing on protocols that cross first-order and continuous quantum transitions, both in finite-size systems and in the thermodynamic limit. As a paradigmatic example, we consider the quantum Ising chain in the presence of homogeneous transverse ($g$) and longitudinal ($h$) magnetic fields. This model exhibits a continuous quantum transition (CQT) at $g=g_c$ and $h=0$, and first-order quantum transitions (FOQTs) driven by $h$ along the line $h=0$ ($g<g_c$). In the integrable limit $h=0$, the system can be mapped onto a quadratic fermionic theory; however, any nonvanishing longitudinal field breaks integrability and the spectrum of the resulting Hamiltonian is generally expected to enter a chaotic regime. We analyze QQs in which the longitudinal field is suddenly changed from a negative value $h_i < 0$ to a positive value $h_f>0$. We focus on values of $h_f$ such that the spectrum of the post-QQ Hamiltonian $H(g,h_f)$ lies in the chaotic regime, where thermalization may emerge at asymptotically long times. We study the out-of-equilibrium dynamics for different values of $g$, finding qualitatively distinct behaviors for $g > g_c$ (where the chain is in the disordered phase), for $g = g_c$ (QQ across the CQT), and for $g<g_c$ (QQ across the FOQT line).