Dynamical instabilities and transient short-range order in the fermionic Hubbard model

TL;DR

This paper investigates the non-equilibrium dynamics of magnetic correlations in the fermionic Hubbard model after a rapid interaction ramp, revealing transient short-range order and different dynamical regimes through advanced theoretical methods.

Contribution

The study introduces a combined Schwinger-Keldysh and Bethe-Salpeter approach to analyze magnetic correlation dynamics in the Hubbard model, highlighting transient short-range order phenomena.

Findings

Identification of a transient short-range ordered regime

Dependence of dynamical behavior on ramping time and interaction strength

Proposal for experimental observation in ultracold atom systems

Abstract

We study the dynamics of magnetic correlations in the half-filled fermionic Hubbard model following a fast ramp of the repulsive interaction. We use Schwinger-Keldysh self-consistent second-order perturbation theory to investigate the evolution of single-particle Green's functions and solve the non-equilibrium Bethe-Salpeter equation to study the dynamics of magnetic correlations. This approach gives us new insights into the interplay between single-particle relaxation dynamics and the growth of antiferromagnetic correlations. Depending on the ramping time and the final value of the interaction, we find different dynamical behavior which we illustrate using a dynamical phase diagram. Of particular interest is the emergence of a transient short-range ordered regime characterized by the strong initial growth of antiferromagnetic correlations followed by a decay of correlations upon thermalization. The discussed phenomena can be probed in experiments with ultracold atoms in optical lattices.