Entanglement-enhanced correlation propagation in the one-dimensional SU($N$) Fermi-Hubbard model

TL;DR

This paper studies how entanglement influences the speed of correlation spread in a one-dimensional SU(N) Fermi-Hubbard model after a quench, revealing collective enhancement effects for N>2.

Contribution

It introduces an analytical model linking entanglement to increased propagation velocity and confirms this with numerical simulations for multiple N values.

Findings

Entanglement enhances correlation propagation velocity for N>2.

Propagation velocity approaches Bose-Hubbard limit as N increases.

Numerical results support analytical predictions across different N.

Abstract

We investigate the dynamics of correlation propagation in the one-dimensional Fermi-Hubbard model with SU($N$) symmetry when the replusive-interaction strength is quenched from a large value, at which the ground state is a Mott-insulator with $1/N$ filling, to an intermediate value. From approximate analytical insights based on a simple model that captures the essential physics of the doublon excitations, we show that entanglement in the initial state leads to collective enhancement of the propagation velocity $v_{\text{SU}(N)}$ when $N>2$, becoming equal to the velocity of the Bose-Hubbard model in the large-$N$ limit. These results are supported by numerical calculations of the density-density correlation in the quench dynamics for $N=2,3,4,$ and $6$.