Entanglement entropy and computational complexity of the Anderson impurity model out of equilibrium I: quench dynamics

Abstract

We study the growth of entanglement entropy in density matrix renormalization group calculations of the real-time quench dynamics of the Anderson impurity model. We find that with appropriate choice of basis, the entropy growth is logarithmic in both the interacting and noninteracting single-impurity models. The logarithmic entropy growth is understood from a noninteracting chain model as a critical behavior separating regimes of linear growth and saturation of entropy, corresponding respectively to an overlapping and gapped energy spectra of the set of bath states. We find that with an appropriate choices of basis (energy-ordered bath orbitals), logarithmic entropy growth is the generic behavior of quenched impurity models. A noninteracting calculation of a double-impurity Anderson model supports the conclusion in the multi-impurity case. The logarithmic growth of entanglement entropy enables studies of quench dynamics to very long times.