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

TL;DR

We study correlation propagation in the one-dimensional SU($N$) Fermi-Hubbard model after a quench from $U/J \to \infty$ to a finite $U/J$, starting from a $1/N$-filled Mott insulator. We develop an analytical picture based on doublon-holon excitations showing that entanglement in the initial state leads to collective enhancement of the propagation velocity $v_{\text{SU}(N)}$ for $N>2$, approaching the Bose-Hubbard (SCBHM) velocity in the large-$N$ limit. We corroborate this with matrix-product-state based simulations (DMRG initial state and TEBD-like time evolution) observing light-cone-like spreading in the density-density correlator $D(r,t)$ with a velocity increasing with $N$; no enhancement occurs for $N=2$ or for simple product initial states. The results reveal entanglement in the initial flavor sector as a mechanism for faster information spreading in SU($N$) 1D Fermi-Hubbard systems, and offer a route to explore the crossover to bosonic-like transport in experiments.

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 $6$.

Figures (3)

• Figure 1: Illustration of a simple two-site model for SCBHM, SU(2) and SU(3) FHM (for simplicity we restrict SU(3) to the ground-state symmetry sector $N_{\rm A}=N_{\rm B}=N_{\rm C}=1$). The green, blue and red circles correspond to different flavors, while the empty circle corresponds to a hole (an empty site). We can define the SU(2) and SU(3) equal-superposition collective doublon and holon states as $|d_j \rangle = \frac{1}{\sqrt{N}}\sum_{\nu=1}^{N} |d_{j,\nu}\rangle$ and $|h_j \rangle = \frac{1}{\sqrt{N}}\sum_{\nu=1}^{N} |h_{j,\nu}\rangle$, where $j=1,2$.
• Figure 2: (a)-(f) shows $\tilde{D}(r,t)$ of systems time-evolved with a final Hamiltonian that has $U_{\rm fin}/J=8$ for several distances $r$. The curves for different $r$ are shifted for clarity by $r$. (a),(c-f) shows this for initial states which are ground states of $U_{\rm ini}/J=40$ for the respective Hamiltonian types SU(2) (a), SU(6) (c), SU(3) (d), SU(4) FHM (e) and SCBHM (f) , while (b) shows the ABCD initial state time-evolved by the SU(4) Hamiltonian. For SU(6), we consider $L=12$, while $L=24$ in all the other cases. (g) shows the velocities $v \hbar/ aJ$ extracted by a fitting for $U_{\rm ini}/J=40$ and $U_{\rm fin}/J=8$ when $L=12$ and $24$. (h) shows fitted velocities $v \hbar/ aJ$ for different values of $U_{\rm fin}/J$ when $L=24,U_{\rm ini}/J=40$ (the ABCD case has no value $U_{\rm ini}/J$). The magenta squares correspond to SU(2), green left-facing triangles to ABCD, the blue diamonds to SU(3), the red circles to SU(4) and the black right-facing triangles to the SCBHM.
• Figure S1: The numerical spectrum for the restricted Fock spaces corresponding to the holon (a) and doublon (b) models for SU(3) with $N_{\rm P}=9$.