Toward accurate and efficient nonequilibrium quantum dynamics of lattice models

Lattice models (e.g., Holstein, Hubbard, and Ising) are ubiquitously used to study the nonequilibrium quantum dynamics of energy and charge transport in materials. Yet, simulating their exact quantum dynamics remains a fundamental challenge. While sophisticated solvers based on tensor networks and path integrals can be applied to interrogate the dynamics of such systems, these methods generally scale exponentially or, at best, polynomially with system size and simulation time, limiting their application to small system sizes and short simulation times. This prevents researchers from accessing the transition between nonequilibrium relaxation and the onset of near-equilibrium transport. In this talk, I will present our space- and time-local generalized master equation (STL-GME), which leverages simulations of small lattices over short times to exactly simulate the dynamics of macroscopic systems over arbitrary times. This enables us to bridge the nonequilibrium and thermodynamic limits. I will illustrate its application to nonequilibrium polaron formation and relaxation dynamics in one-dimensional (1D) and two-dimensional (2D) dispersive Holstein lattices. I will show how variations in energy scales affect polaron motion, which recent microscopy experiments on transition metal oxides and organic semiconductors can track.