Quench dynamics of stripes and phase separation in the two-dimensional $t$-$J$ model

TL;DR

This study explores the nonequilibrium dynamics of the two-dimensional $t$-$J$ model after a chemical potential quench, revealing distinct behaviors in stripe and phase-separated regimes, including stable charge patterns and dynamical freezing.

Contribution

It provides the first detailed analysis of the real-time evolution of charge and entanglement in the $t$-$J$ model across different phases using advanced numerical methods.

Findings

Charge density spreads ballistically in the stripe phase.

Charge degrees of freedom freeze in the phase-separated regime.

Entanglement entropy remains bounded in the phase-separated regime.

Abstract

We investigate the fundamental dynamical process of an initial quench of the chemical potential of the two-dimensional $t$-$J$ model. Depending on the ground state phase, sharply different dynamical behavior of the charge distribution and entanglement properties are observed. In the stripe phase, the intertwining of the spin and charge density waves remains stable under time evolution. A ballistic spreading of the charge density is observed with a propagation speed that is only weakly dependent on the coupling ratio, $J/t$. Moreover, in the phase-separated regime for large $J/t$, we report a complete dynamical freezing of charge degrees of freedom within, where even under long time evolution the entanglement entropy remains bounded. Our results are obtained by combining large-scale exact diagonalizations and matrix product state techniques for time evolution.