The Cluster Generalization of the Truncated Wigner Approximation for interacting spin lattices

This talk will detail a generalization of the Truncated Wigner Approximation (TWA) through systematic inclusion of entanglement degrees of freedom in a semi-classical phase space. Linear quantum dynamics is replaced by classical nonlinear dynamics, where difficulty is polynomial instead of exponential in system size. Observables, entanglement and quantum correlations are encoded in the phase space via nonlinear evolution. We demonstrate the method on many-body systems of interacting spins, reproducing essential features in both the Many Body Localized and Thermalizing regimes.