Quantum critical dynamics in two-dimensional transverse Ising model

TL;DR

This study investigates quantum critical dynamics in a two-dimensional transverse Ising model, revealing how universal critical behavior influences quantum dynamics and dielectric properties near the quantum critical point.

Contribution

It introduces a kinetic protocol based on quantum Monte Carlo to analyze quantum dynamics near the QCP in a transverse Ising model on a triangular lattice.

Findings

Dynamical susceptibility follows a Debye function form.

Peak-narrowing of susceptibility near QCP due to diverging relaxation times.

Material exhibits dielectric anomalies consistent with proximity to ferroelectric QCP.

Abstract

In the vicinity of the quantum critical point(QCP), thermodynamic properties diverge toward zero temperature governed by universal exponents. Although this fact is well known, how it is reflected in quantum dynamics has not been addressed. As an ideal experimental platform to test the issue, we consider an organic Mott insulator whose dielectric degrees of freedom, a quantum electric dipole, is described by the transverse Ising model on a triangular lattice that has a QCP. We track the Glauber-type dynamics of the model by constructing a kinetic protocol based on the quantum Monte Carlo method. The dynamical susceptibility takes the form of the Debye function and shows a significant peak-narrowing in approaching a QCP due to the divergence of the relaxation timescale. It resembles the anomaly of dielectric constants observed in the organic materials \k{appa}-ET 2 X dimer Mott insulating phase, indicating that the material is very near the ferroelectric QCP.