Double resonance in the infinite-range quantum Ising model

TL;DR

This paper investigates the quantum resonance phenomena in the infinite-range quantum Ising model at zero temperature, revealing the occurrence of double resonance peaks related to the energy gap and phase transition.

Contribution

It demonstrates that double resonance peaks are a generic feature of continuous phase transitions in quantum many-body systems, supported by numerical analysis.

Findings

Two resonance peaks occur at specific transverse field strengths.

Resonance peaks align with the energy gap matching the external frequency.

Double resonance is proposed as a universal feature of continuous transitions.

Abstract

We study quantum resonance behavior of the infinite-range kinetic Ising model at zero temperature. Numerical integration of the time-dependent Schr\"odinger equation in the presence of an external magnetic field in the $z$ direction is performed at various transverse field strengths $g$. It is revealed that two resonance peaks occur when the energy gap matches the external driving frequency at two distinct values of $g$, one below and the other above the quantum phase transition. From the similar observations already made in classical systems with phase transitions, we propose that the double resonance peaks should be a generic feature of continuous transitions, for both quantum and classical many-body systems.