Post-quench relaxation dynamics of Gross-Neveu lattice fermions

TL;DR

We investigate post-quench relaxation in a lattice $N$-flavor Gross-Neveu model using a time-dependent self-consistent mean-field (SCMF) approach coupled to a Lindblad master equation to incorporate environment effects via $\gamma$. In the closed case ($\gamma=0$), the global order parameter $m(t)$ exhibits persistent oscillations and revivals in finite systems, consistent with ETH in the thermodynamic limit for the long-time value, while finite-momentum correlators do not relax. Introducing a finite system–environment coupling ($\gamma>0$) drives all observables, including correlation functions, toward stationary values, with revivals suppressed and damping observed. The study highlights distinct relaxation channels for global versus finite-momentum observables and provides a practical framework to steer toward target states by tuning quench protocols and dissipation in open quantum many-body systems.

Abstract

We study the quantum relaxation dynamics for a lattice version of the one-dimensional (1D) $N$-flavor Gross-Neveu (GN) model after a Hamiltonian parameter quench. Allowing for a system-reservoir coupling $γ$, we numerically describe the system dynamics through a time-dependent self-consistent Lindblad master equation. For a closed ($γ=0$) finite-size system subjected to an interaction parameter quench, the order parameter dynamics exhibits oscillations and revivals. In the thermodynamic limit, our results imply that the order parameter reaches its post-quench stationary value in accordance with the eigenstate thermalization hypothesis (ETH). However, time-dependent finite-momentum correlation matrix elements equilibrate only if $γ>0$. Our findings highlight subtle yet important aspects of the post-quench relaxation dynamics of quantum many-body systems.

Figures (10)

• Figure 1: Equilibrium phase diagram of the lattice GN model \ref{['mh.1']} in the $g$-$T$ plane. Here $J=1$ sets the energy unit and we use $L=2000$ sites. We assume the large-$N$ limit, where SCMF theory becomes exact. The solid curve marks the phase boundary between the ordered ($m\ne 0$) and the disordered ($m=0$) phase. As no significant changes are observed upon further increasing $L$, these results essentially correspond to the thermodynamic limit.
• Figure 2: Post-quench order parameters $m(t)$ (left) and $\delta J(t)$ (right column) vs time $t$ for a closed GN model in the large-$N$ limit where SCMF theory becomes exact. Units are determined by $J=1$. The quench at $t=0$ is performed in the interaction strength, $g=g_i\to g=g_f$, with $g_i=1$ in all panels. Results were obtained by numerically solving Eqs. \ref{['LME.3']}, \ref{['LME.4']} and \ref{['LME.5']} for $L=100$, using (a) $g_f=0.9$, (b) $g_f=0.6$, and (c) $g_f=0.5$.
• Figure 3: Post-quench order parameters $m(t)$ (left) and $\delta J(t)$ (right column) vs time $t$ for a closed GN system as in Fig. \ref{['fig2']}(b) with $g_f=0.6$, but for different values of $L$. To better highlight the oscillations in $m(t)$ and $\delta J(t)$, we omit the initial drop at $t=0^+$ visible in Fig. \ref{['fig2']} in this and the following figures. Results are shown for (a) $L=100$, (b) $L=200$, and (c) $L=400$.
• Figure 4: Post-quench dynamics of $m(t)$ (left) and $\delta J(t)$ (right column) for the closed GN model with different $L$ as in Fig. \ref{['fig3']} but for $g_f=0.5$, see also Fig. \ref{['fig2']}(c). Results are shown for (a) $L=100$, (b) $L=200$, and (c) $L=400$.
• Figure 5: Post-quench dynamics of $m(t)$ (left) and $\delta J(t)$ (right column) vs time $t$ (in units with $J=1$) without enforcing time-dependent self-consistency. As for the self-consistent counterpart in Fig. \ref{['fig3']}, we consider a quench from $g_i=1$ to $g_f=0.6$ for (a) $L=100$, (b) $L=200$, and (c) $L=400$.