Entanglement entropy of disordered quantum chains following a global quench

TL;DR

This paper investigates how entanglement entropy evolves over time in disordered quantum chains after a global quench, providing numerical evidence for many-body localization in bond-disordered systems.

Contribution

It offers the first numerical evidence for many-body localization in bond-disordered systems and compares entanglement growth under different disorder types.

Findings

Entanglement entropy grows logarithmically in time in certain disordered systems.

Multiprecision calculations are necessary to observe the correct scaling regimes.

Evidence suggests a many-body localized phase in bond-disordered quantum chains.

Abstract

We numerically investigate the growth of the entanglement entropy S_{ent}(t) in time t---after a global quench from a product state---in quantum chains with various kinds of disorder. The main focus is, in particular, on fermionic chains with bond disorder. In the noninteracting case at criticality we numerically test recent predictions by the real space renormalization group for the entanglement growth in time, the maximal entanglement as a function of block size, and the decay of a density wave order parameter. We show that multiprecision calculations are required to reach the scaling regime and perform such calculations for specific cases. For interacting models with binary bond disorder we present data based on infinite size density matrix renormalization group calculations and exact diagonalizations. We obtain first numerical evidence for a many-body localized phase in bond disordered systems where S_{ent}(t)~ln t$ seems to hold. Our results for bond disorder are contrasted with the well studied case of potential disorder.