Dynamics of a quantum phase transition with decoherence: the quantum Ising chain in a static spin environment

TL;DR

This paper investigates how decoherence and non-adiabatic effects influence the dynamics of a quantum phase transition in the Ising chain, revealing how excitation energy, fidelity, and correlations evolve under different quench rates and environmental interactions.

Contribution

It introduces a detailed analysis of the interplay between decoherence and non-adiabaticity during a quantum phase transition in the Ising chain, highlighting new decay behaviors and correlation patterns.

Findings

Excitation energy decays as inverse square root of quench time for weak decoherence and fast quenches.

Fidelity decays exponentially with chain size, with a rate linked to excited kink density.

Kink correlations transition from anti-bunching to Poissonian distribution along the chain.

Abstract

We consider a linear quench from the paramagnetic to ferromagnetic phase in the quantum Ising chain interacting with a static spin environment. Both decoherence from the environment and non-adiabaticity of the evolution near a critical point excite the system from the final ferromagnetic ground state. For weak decoherence and relatively fast quenches the excitation energy, proportional to the number of kinks in the final state, decays like an inverse square root of a quench time, but slow transitions or strong decoherence make it decay in a much slower logarithmic way. We also find that fidelity between the final ferromagnetic ground state and a final state after a quench decays exponentially with a size of a chain, with a decay rate proportional to average density of excited kinks, and a proportionality factor evolving from 1.3 for weak decoherence and fast quenches to approximately 1 for slow transitions or strong decoherence. Simultaneously, correlations between kinks randomly distributed along the chain evolve from a near-crystalline anti-bunching to a Poissonian distribution of kinks in a number of isolated Anderson localization centers randomly scattered along the chain.