Capturing spin chain dynamics with periodically projected time-dependent basis

Abstract

Simulating many-body quantum systems poses significant challenges due to the large size of the state space. To address this issue, we propose using an SU(2) coherent state for individual spins to simulate spins on a lattice and derive equations of motion based on the variational principle. This method involves a sampling approach, where a subset of relevant configurations is chosen based on energy criteria, and a projection method is used to remove linear dependency on the overcomplete and time-dependent basis during propagation. We validate this method through numerical simulations of up to seven-qubit system, calculating key physical observables such as state probabilities and domain-wall densities. Our results indicate that while complete basis sets offer accurate dynamics, selected incomplete sets can recover essential features, especially with the assistance of a projector. The selected incomplete dual bases method is not limited by the structure of Hamiltonian and efficiently captures the non-equilibrium dynamics.