Anomalous Behavior of Magnetic Susceptibility Obtained by Quench Experiments in Isolated Quantum Systems

TL;DR

This paper explores the relationship between quench-induced magnetic susceptibility and thermodynamic susceptibilities in isolated quantum systems, revealing discontinuities and providing experimental predictions for spin chain systems.

Contribution

It proves the discontinuity of quench susceptibility at zero wave vector and links it to thermodynamic susceptibilities under certain conditions, with numerical predictions for experimental observation.

Findings

Quench susceptibility is discontinuous at k=0 in translationally invariant systems.

Values at k=0 and approaching zero match adiabatic and isothermal susceptibilities.

Predictions for observing these behaviors in XYZ spin chain experiments.

Abstract

We examine how the magnetic susceptibility obtained by the quench experiment on isolated quantum systems is related to the isothermal and adiabatic susceptibilities defined in thermodynamics. Under the conditions similar to the eigenstate thermalization hypothesis, together with some additional natural ones, we prove that for translationally invariant systems the quench susceptibility as a function of wave vector k is discontinuous at k=0. Moreover, its values at k=0 and the k to 0 limit coincide with the adiabatic and the isothermal susceptibilities, respectively. We give numerical predictions on how these particular behaviors can be observed in experiments on the XYZ spin chain with tunable parameters, and how they deviate when the conditions are not fully satisfied.