# Zeros of Loschmidt echo in the presence of Anderson localization

## TL;DR

This paper investigates the behavior of the Loschmidt echo and dynamical free energy in the Anderson model after a disorder quench, revealing periodic zeros linked to localization phenomena and connecting dynamical phase transitions with localization-delocalization transitions.

## Contribution

It introduces a novel analysis of Loschmidt echo zeros in Anderson localization, showing their periodic nature and relation to spectral width, supported by numerical evidence.

## Key findings

- Loschmidt echo exhibits periodic zeros in localized regimes
- Dynamical free energy diverges logarithmically at zeros
- Zeros are connected to spectral width and phase transitions

## Abstract

We study the Loschmidt echo and the dynamical free energy of the Anderson model after a quench of the disorder strength. If the initial state is extended and the eigenstates of the post-quench Hamiltonian are strongly localized, we argue that the Loschmidt echo exhibits zeros periodically with the period $2\pi /D$ where $D$ is the width of spectra. At these zeros, the dynamical free energy diverges in a logarithmic way. We present numerical evidence of our argument in one- and three-dimensional Anderson models. Our findings connect the dynamical quantum phase transitions to the localization-delocalization phase transitions.