Algebraic versus exponential decoherence in dissipative many-particle systems

TL;DR

This paper compares algebraic and exponential decoherence in dissipative quantum spin chains, revealing that the nature of decoherence depends on the model and internal interactions, with algebraic decay occurring in the open XXZ model and exponential decay in the transverse-field Ising model.

Contribution

It demonstrates how internal interactions influence decoherence types in quantum many-body systems, highlighting the divergence of decoherence time in the open XXZ model and contrasting it with exponential decay in the Ising model.

Findings

Decoherence time diverges in the thermodynamic limit for the open XXZ model.

Decoherence is algebraic in the open XXZ model due to a vanishing Liouville spectrum gap.

Decoherence remains exponential in the open transverse-field Ising model.

Abstract

The interplay between dissipation and internal interactions in quantum many-body systems gives rise to a wealth of novel phenomena. Here we investigate spin-1/2 chains with uniform local couplings to a Markovian environment using the time-dependent density matrix renormalization group (tDMRG). For the open XXZ model, we discover that the decoherence time diverges in the thermodynamic limit. The coherence decay is then algebraic instead of exponential. This is due to a vanishing gap in the spectrum of the corresponding Liouville superoperator and can be explained on the basis of a perturbative treatment. In contrast, decoherence in the open transverse-field Ising model is found to be always exponential. In this case, the internal interactions can both facilitate and impede the environment-induced decoherence.