Emergent Spatial Textures from Interaction Quenches in the Hubbard Model

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.

Figures (9)

• Figure 1: GvND dynamics following an interaction quench to final strength $U_f$. Panels (a)--(c) show the time evolution of the double occupancy $\mathcal{D}(t)$ and its spatial standard deviation $\sigma_{\mathcal{D}}(t)$ for weak, intermediate, and strong quenches. Panel (d) shows the oscillation period $\mathcal{T}$ extracted from the early-time dynamics as a function of $U_f/W$. Panel (e) shows the early-time and long-time averaged double occupancy $D^*$ with varying $U_f$.
• Figure 2: Snapshots of the spatial distribution of the double occupancy $\mathcal{D}(x,y)$ at intermediate time $t=500$ and long time $t=6000$ for interaction strength $U_f/W=0.22$. The corresponding distributions of $\mathcal{D}$ are shown in the insets.
• Figure 3: Snapshots of the spatial distribution of the double occupancy $\mathcal{D}(x,y)$ at intermediate time $t=80$ and long time $t=5000$ for interaction strength $U_f/W=1.0$. The corresponding distributions of $\mathcal{D}$ are shown in the insets.
• Figure 4: Coarsening dynamics following a quench to $U_f/W=0.72$. (a) Time evolution of the spatially averaged double occupancy $\mathcal{D}(t)$, its spatial standard deviation $\sigma_{\mathcal{D}}(t)$, and the density fluctuation $\sigma_n(t)$. (b)–(e) Snapshots of the local double occupancy $\mathcal{D}_i$ at the indicated times, showing domain nucleation followed by coarsening. Insets show the corresponding distributions of $\mathcal{D}_i$.
• Figure 5: Probability distributions of the local double occupancy $\mathcal{D}_i(t)$ constructed from all sites of a $48\times48$ lattice and averaged over the time window $t\in[1000,1100]$. Panels (a)–(c) correspond to quenches in the weak-, intermediate-, and strong-coupling regimes, respectively.