Non-monotonic Dynamics in Frustrated Ising Model with Time-Dependent Transverse Field

TL;DR

This paper investigates non-monotonic behaviors in spin correlation functions within frustrated Ising models under thermal and quantum fluctuations, revealing complex dynamics and dependence on field sweep rates.

Contribution

It demonstrates non-monotonic correlation functions in both classical and quantum frustrated systems and explores their real-time dynamics under time-dependent fields.

Findings

Correlation functions show non-monotonic temperature dependence.

Ground state correlation also non-monotonic with transverse field.

Slow field sweeps induce non-monotonic changes in quantum systems.

Abstract

We study how the degree of ordering depends on the strength of the thermal and quantum fluctuations in frustrated systems by investigating the correlation function of the order parameter. Concretely, we compare the equilibrium spin correlation function in a frustrated lattice which exhibits a non-monotonic temperature dependence (reentrant type dependence) with that in the ground state as a function of the transverse field that causes the quantum fluctuation. We find the correlation function in the ground state also shows a non-monotonic dependence on the strength of the transverse field. We also study the real-time dynamics of the spin correlation function under a time-dependent field. After sudden decrease of the temperature, we found non-monotonic changes of the correlation function reflecting the static temperature dependence, which indicates that an effective temperature of the system changes gradually. For the quantum system, we study the dependence of changes of the correlation function on the sweeping speed of the transverse field. Contrary to the classical case, the correlation function varies little in a rapid change of the field, though it shows a non-monotonic change when we sweep the field slowly.