Singular ferromagnetic susceptibility of the transverse-field Ising antiferromagnet on the triangular lattice

TL;DR

This study investigates the singular behavior of ferromagnetic susceptibility in the power-law ordered phase of the transverse-field Ising antiferromagnet on a triangular lattice, revealing a novel finite-size scaling and field response.

Contribution

The paper introduces a quantum cluster algorithm to analyze ferromagnetic susceptibility and confirms a predicted singular L dependence in the power-law phase.

Findings

Ferromagnetic susceptibility scales as L^{2-9η} in the intermediate phase.

Susceptibility to a uniform field diverges as |B|^{-(4-18η)/(4-9η)} at small B.

No ferromagnetic long-range order exists at low temperature.

Abstract

A transverse magnetic field $\Gamma$ is known to induce antiferromagnetic three-sublattice order of the Ising spins $\sigma^z$ in the triangular lattice Ising antiferromagnet at low enough temperature. This low-temperature order is known to melt on heating in a two-step manner, with a power-law ordered intermediate temperature phase characterized by power-law correlations at the three-sublattice wavevector ${\bf Q}$: $\langle \sigma^z(\vec{R}) \sigma^z(0)\rangle \sim \cos({\mathbf Q}\cdot \vec{R}) /|\vec{R}|^{\eta(T)}$ with the temperature-dependent power-law exponent $\eta(T) \in (1/9,1/4)$. Here, we use a newly developed quantum cluster algorithm to study the {\em ferromagnetic} easy-axis susceptibility $\chi_{u}(L)$ of an $L \times L$ sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular $L$ dependence $\chi_{u}(L)\sim L^{2- 9 \eta}$ when $\eta(T)$ is in the range $(1/9,2/9)$. This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility $\chi_{u}(B)$ to a uniform field $B$ along the easy axis is singular at intermediate temperatures in the small $B$ limit, $\chi_{u}(B) \sim |B|^{-\frac{4 - 18 \eta}{4-9\eta}}$ for $\eta(T) \in (1/9, 2/9)$, although there is no ferromagnetic long-range order in the low temperature state.