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

## TL;DR

This paper demonstrates that in the Anderson impurity model, entanglement entropy grows logarithmically during quench dynamics, facilitating long-time simulations, with the behavior explained via a noninteracting chain model and basis optimization.

## Contribution

It shows that logarithmic entanglement growth is generic in quenched impurity models when using energy-ordered bath orbitals, enabling extended real-time studies.

## Key findings

- Logarithmic entropy growth observed in both interacting and noninteracting models.
- Entropy growth behavior explained by a critical transition in the energy spectrum.
- Basis choice significantly affects the entropy growth pattern.

## 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.