Loschmidt echo and Momentum Distribution in a Kitaev Spin Chain

TL;DR

This paper studies the Loschmidt echo and momentum distribution in a Kitaev spin chain, revealing size-dependent revival phenomena and effects of initial magnon states, with implications for quantum criticality and dynamical behavior.

Contribution

It introduces analysis of Loschmidt echo dynamics in a Kitaev chain with both constant and kicked magnetic fields, highlighting size effects and critical point phenomena.

Findings

Long-time revival peaks depend on chain length and initial magnon states.

Momentum distribution maxima relate to initial magnon momenta and decay as 1/N.

Kicked magnetic fields influence Loschmidt echo evolution, with special periods causing no evolution.

Abstract

We investigate the Loschmidt echo in a one-dimensional spin chain having Kitaev-type interaction in constant and kicked magnetic fields. The Loschmidt echo for the initial states having different magnon excitations shows long-time revivals for smaller chains and has short-time revival peaks for the longer chains. The system near the critical point shows peculiarly long-time revival peaks of the Loschmidt echo for relatively larger chains. The presence of a magnon in the initial state affects the Loschmidt echo revival peaks. The momentum distribution function exhibits maxima for a few momenta that are associated with the momentum of the magnon excitation present in the initial states. The probability maxima decay as O(1/N ) with the system size. For the Hamiltonian with kicked magnetic fields, the Loschmidt echo depends on the kick period. For a special kick period, the Loschmidt echo shows no evolution at all irrespective of the system size.