Density dynamics in the mass-imbalanced Hubbard chain

Abstract

We consider two mutually interacting fermionic particle species on a one-dimensional lattice and study how the mass ratio $\eta$ between the two species affects the (equilibration) dynamics of the particles. Focussing on the regime of strong interactions and high temperatures, two well-studied points of reference are given by (i) the case of equal masses ${\eta = 1}$, i.e., the standard Fermi-Hubbard chain, where initial non-equilibrium density distributions are known to decay, and (ii) the case of one particle species being infinitely heavy, ${\eta = 0}$, leading to a localization of the lighter particles in an effective disorder potential. Given these two opposing cases, the dynamics in the case of intermediate mass ratios ${0 < \eta < 1}$ is of particular interest. To this end, we study the real-time dynamics of pure states featuring a sharp initial non-equilibrium density profile. Relying on the concept of dynamical quantum typicality, the resulting non-equilibrium dynamics can be related to equilibrium correlation functions. Summarizing our main results, we observe that diffusive transport occurs for moderate values of the mass imbalance, and manifests itself in a Gaussian spreading of real-space density profiles and an exponential decay of density modes in momentum space. For stronger imbalances, we provide evidence that transport becomes anomalous on intermediate time scales and, in particular, our results are consistent with the absence of strict localization in the long-time limit for any ${\eta > 0}$. Based on our numerical analysis, we provide an estimate for the "lifetime" of the effective localization as a function of $\eta$.