Condensed Matter Seminar: Influence matrices for quantum dynamics: phase transitions in and out of equilibrium

The Feynman-Vernon influence functional encodes the full effect of an environment on a quantum system. Recasting it as a compressed spacetime tensor network, the influence matrix, opens new ways to study quantum dynamics. Having established influence matrices as a state-of-the-art method for real-time evolution of quantum impurities, we focus on the two-impurity Anderson model. We are able to simultaneously capture the short-time transient dynamics and the diverging time scales around a two-channel Kondo critical point hosting an emergent Majorana (Lotem et al., arXiv:2607.16411). Influence matrices also serve as diagnostic tools, as we demonstrate by studying the temporal-entanglement structure of the driven XXZ spin chain. Preliminary results suggest that the experimentally observed ballistic-to-diffusive transition is accompanied by temporal spontaneous magnetic symmetry breaking.