A time and spatially resolved quench of the fermionic Hubbard model showing restricted equilibration

TL;DR

This paper studies the non-equilibrium dynamics of fermionic Hubbard models after a quench, revealing restricted thermalization, oscillatory decay, and linear information propagation, using advanced quantum Monte Carlo methods.

Contribution

It demonstrates the use of Gaussian properties and quantum Monte Carlo techniques to simulate large-scale fermionic systems post-quench, providing numerically exact insights into their relaxation behavior.

Findings

Final states resemble thermal single-particle density matrices.

Decay towards equilibrium is oscillatory with a power-law component.

Charge and spin correlations propagate linearly with velocity ~4.

Abstract

We investigate the quench of half-filled 1D and 2D fermionic Hubbard models to models without Coulomb interaction. Since the time propagation is gaussian we can use a variety of time-dependent quantum Monte Carlo methods to tackle this problem without generating a dynamical sign problem. Using a continuous time quantum Monte Carlo method (CTQMC) we achieve a system size of 128 sites in 1D, and using a Blankenbecler-Scalapino-Sugar (BSS) type algorithm we were able to simulate 20 x 20 square lattices. Applying these methods to study the dynamics after the quench, we observe that the final state of the system can be reasonably well described by a thermal single-particle density matrix that takes the initial single particle conservation laws into account. The characteristic decay towards this limit is found to be oscillatory with an additional power law decay that depends on the dimensionality. This numerically exact result is shown to compare favorable to mean-field approximations as well as to perturbation theory. Furthermore we observe the information propagation in the 1D-case in the charge charge and spin spin correlations and find that it is linear with a velocity of roughly v = 4 in units of the hopping amplitude.