Investigation of a universal behavior between N\'eel temperature and staggered magnetization density for a three-dimensional quantum antiferromagnet

TL;DR

This study uses Monte Carlo simulations to explore a universal relation between Néel temperature and staggered magnetization in a 3D quantum antiferromagnet, confirming the relation and examining logarithmic corrections near the quantum critical point.

Contribution

It provides the first-principles Monte Carlo verification of the universal relation between $T_N/ oot3 ext{c}$ and ${ m f M}_s$ in a 3D quantum antiferromagnet, including effects of spatial anisotropy.

Findings

Monte Carlo results agree with series expansion data.

Universal relation holds near the quantum critical point.

Logarithmic corrections are significant only in strongly anisotropic regimes.

Abstract

We simulate the three-dimensional quantum Heisenberg model with a spatially anisotropic ladder pattern using the first principles Monte Carlo method. Our motivation is to investigate quantitatively the newly established universal relation $T_N/\sqrt{c^3}$ $\propto$ ${\cal M}_s$ near the quantum critical point (QCP) associated with dimerization. Here $T_N$, $c$, and ${\cal M}_s$ are the N\'eel temperature, the spinwave velocity, and the staggered magnetization density, respectively. For all the physical quantities considered here, such as $T_N$ and ${\cal M}_s$, our Monte Carlo results agree nicely with the corresponding results determined by the series expansion method. In addition, we find it is likely that the effect of a logarithmic correction, which should be present in (3+1)-dimensions, to the relation $T_N/\sqrt{c^3}$ $\propto$ ${\cal M}_s$ near the investigated QCP only sets in significantly in the region with strong spatial anisotropy.