Loschmidt echo of local dynamical processes in integrable and non integrable spin chains

TL;DR

This paper studies how the Loschmidt echo reveals differences in local dynamical processes between integrable and non-integrable spin chains, showing sensitivity to quantum disturbance types and background chaos.

Contribution

It demonstrates the Loschmidt echo's ability to differentiate integrable from non-integrable dynamics and its dependence on quantum disturbance parameters and timing.

Findings

Higher revival probability for incoherent QDPs at large times in integrable systems

Decaying Loschmidt echo in non-integrable systems with slower decay in less chaotic regimes

Loschmidt echo effectively distinguishes between integrable and non-integrable dynamics during QDPs

Abstract

The Loschmidt echo is investigated to track the effect of the local QDP. It is also quite sensitive to whether the background dynamics is integrable or not. For the integrable case, viz. the Heisenberg model, the Loschmidt echo depends on the parameters operators corresponding to the QDP as well as the time of QDP. The probability of reviving the system to its initial state is higher for incoherent QDPs occurring at large time intervals. Whereas each time coherent QDP occurs certain probability of reviving the state is always lost. For For the non-integrable case, viz. a kicked Harper model, it exhibits a decaying behaviour when contrasted with integrable dynamics. The decay rate is slower when the corresponding classical Hamiltonian is non chaotic. The Loschmidt echo also distinguishes the integrable and the nonintegrable dynamics when a QDP occurs.