Emergent Spatial Textures from Interaction Quenches in the Hubbard Model

TL;DR

This paper demonstrates that in the Hubbard model, interaction quenches lead to spontaneous spatial pattern formation, revealing the importance of spatial inhomogeneities in nonequilibrium dynamics of correlated electron systems.

Contribution

It introduces a real-space time-dependent Gutzwiller approach to show that homogeneous dynamics are unstable, leading to inhomogeneous states and spatial self-organization.

Findings

Weak spatial fluctuations grow and induce inhomogeneity.

Post-quench dynamics show domain nucleation and coarsening.

Spatial self-organization is a generic feature of nonequilibrium correlated matter.

Abstract

Interaction quenches in strongly correlated electron systems provide a powerful route to probe nonequilibrium many-body dynamics. For the Hubbard model, nonequilibrium dynamical mean-field theory has revealed coherent post-quench oscillations, dynamical crossovers, and long-lived transient regimes. However, these studies are largely restricted to spatially homogeneous dynamics and therefore neglect the role of spatial structure formation during ultrafast evolution. Here we investigate interaction quenches in the half-filled Hubbard model using a real-space time-dependent Gutzwiller framework. We show that homogeneous nonequilibrium dynamics is generically unstable: even arbitrarily weak spatial fluctuations grow dynamically and drive the system toward intrinsically inhomogeneous states. Depending on the interaction strength, the post-quench evolution exhibits spatial differentiation, nucleation, and slow coarsening of Mott-like domains. Our results establish spatial self-organization as a generic feature of far-from-equilibrium correlated matter and reveal a fundamental limitation of spatially homogeneous nonequilibrium theories.