Transient Loschmidt Echo in Quenched Ising Chains

TL;DR

This paper investigates the behavior of the Loschmidt echo in highly excited quantum Ising chains after local and global quenches, revealing exponential decay indicative of quench-induced decoherence.

Contribution

It introduces a perturbative approach to compute the Loschmidt echo in quenched Ising chains, showing exponential decay contrasting with the power-law decay in low-energy cases.

Findings

Loschmidt echo decays exponentially after quenches

Decoherence scale depends on local potential and bulk excitation energy

Results extend understanding of quench-induced decoherence phenomena

Abstract

We study the response to sudden local perturbations of highly excited Quantum Ising Spin Chains. The key quantity encoding this response is the overlap between time-dependent wave functions, which we write as a two-times Loschmidt echo. Its asymptotics at long time differences contains crucial information about the structure of the highly excited non-equilibrium environment induced by the quench. We compute the Echo perturbatively for a weak local quench but for arbitrarily large global quench, using a cumulant expansion. Our perturbative results suggest that the Echo decays exponentially, rather than power law as in the low-energy Orthogonality Catastrophe, a further example of quench-induced decoherence already found in the case of quenched Luttinger Liquids. The emerging decoherence scale is set by the strenght of the local potential and the bulk excitation energy.