Loschmidt echo with a non-equilibrium initial state: early time scaling and enhanced decoherence

TL;DR

This paper investigates the early-time decay and long-term decoherence of the Loschmidt echo in a non-equilibrium setting, revealing quench-independent decay rates near quantum critical points and enhanced decoherence with large quenches.

Contribution

It introduces a generic short-time scaling law for the Loschmidt echo decay rate in non-equilibrium conditions and analyzes its behavior near quantum critical points.

Findings

Decay rate near QCP is quench-independent at early times

Large quenches lead to increased decoherence at long times

Analytical and numerical verification using transverse Ising chain

Abstract

We study the Loschmidt echo (LE) in a central spin model in which a central spin is globally coupled to an environment (E) which is subjected to a small and sudden quench at $t=0$ so that its state at $t=0^+$, remains the same as the ground state of the initial environmental Hamiltonian before the quench; this leads to a non-equilibrium situation. This state now evolves with two Hamiltonians, the final Hamiltonian following the quench and its modified version which incorporates an additional term arising due to the coupling of the central spin to the environment. Using a generic short-time scaling of the decay rate, we establish that in the early time limit, the rate of decay of the LE (or the overlap between two states generated from the initial state evolving through two channels) close to the quantum critical point (QCP) of E is independent of the quenching. We do also study the temporal evolution of the LE and establish the presence of a crossover to a situation where the quenching becomes irrelevant. In the limit of large quench amplitude the non-equilibrium initial condition is found to result in a drastic increase in decoherence at large times, even far away from a QCP. These generic results are verified analytically as well as numerically, choosing E to be a transverse Ising chain where the transverse field is suddenly quenched.