Dynamical recovery of SU(2) symmetry in the mass-quenched Hubbard model

TL;DR

This study uses non-equilibrium dynamical mean-field theory to analyze how SU(2) symmetry is dynamically restored in a Hubbard model after a mass-imbalance quench, revealing thermalization and decay behaviors.

Contribution

It demonstrates the real-time recovery of SU(2) symmetry in a Hubbard model post-quench and links the symmetry restoration to thermalization processes.

Findings

SU(2) symmetry recovered state is thermalized

Order parameter decays exponentially in weak Coulomb regime

System parameters influence thermalization behavior

Abstract

We use non-equilibrium dynamical mean-field theory with iterative perturbation theory as an impurity solver to study the recovery of $SU(2)$ symmetry in real-time following a hopping integral parameter quench from a mass-imbalanced to a mass-balanced single-band Hubbard model at half-filling. A dynamical order parameter $\gamma(t)$ is defined to characterize the evolution of the system towards $SU(2)$ symmetry. By comparing the momentum dependent occupation from an equilibrium calculation (with the $SU(2)$ symmetric Hamiltonian after the quench at an effective temperature) with the data from our non-equilibrium calculation, we conclude that the $SU(2)$ symmetry recovered state is a thermalized state. Further evidence from the evolution of the density of states supports this conclusion. At the same time, we find the order parameter in the weak Coulomb interaction regime undergoes an approximate exponential decay. We numerically investigate the interplay of the relevant parameters (initial temperature, Coulomb interaction strength, initial mass-imbalance ratio) and their combined effect on the thermalization behavior. Finally, we study evolution of the order parameter as the hopping parameter is changed with either a linear ramp or a pulse. Our results can be useful in strategies to engineer the relaxation behavior of interacting, quantum many-particle systems.