Long-time dynamics of optically pumped metals from projected purification

The non-equilibrium dynamics of matter whose vibrations are excited by light fields may produce electronic phases, such as laser-induced high-transition-temperature superconductivity, that do not exist in equilibrium. Simulation of these systems presents a theoretical challenge because of the absence of separation of energy scales, and is further impeded by the large local Hilbert space dimension associated with vibrational modes. Here we employ a recently introduced approach known as projected purification [SciPost Phys. 10, 058 (2021)] in order to overcome this challenge and use the time-dependent variational principle (TDVP) in matrix-product-state (MPS) manifolds to simulate the dynamics of a metal driven at initial time by a spatially uniform pump that excites dipole-active vibrational modes which couple nonlinearly to electrons. We compare our results to those of [Nat. Commun. 12, 5803 (2021)], finding excellent agreement, and show that access to significantly longer times perhaps extending to the long-time limit is now within reach.