Emergent Spatial Textures from Interaction Quenches in the Hubbard Model

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.

💡 Research Summary

This paper investigates interaction quenches in the half‑filled Hubbard model by employing a real‑space, time‑dependent Gutzwiller approximation (TDGA) that is coupled to a von‑Neumann evolution of the quasiparticle density matrix. The authors refer to this scheme as Gutzwiller‑von‑Neumann dynamics (GvND). They simulate a 48 × 48 triangular lattice, starting from the non‑interacting ground state (U_i = 0) and suddenly switching the on‑site interaction to a finite value U_f at time t = 0. A tiny Anderson disorder potential (10⁻⁵ t_nn) is added to seed spatial fluctuations without explicitly breaking symmetries.

In GvND each lattice site carries local Gutzwiller amplitudes Φ_i(t) that encode the probabilities of empty, singly‑occupied, and doubly‑occupied configurations. These amplitudes renormalize the hopping and on‑site energies of an effective quasiparticle Hamiltonian H_qp(Φ). The quasiparticle density matrix ρ obeys the von‑Neumann equation dρ/dt = i