Universal Scaling of the Neel Temperature of Near-Quantum-Critical Quasi-Two-Dimensional Heisenberg Antiferromagnets

TL;DR

This paper investigates the universal scaling behavior of the Neel temperature in quasi-two-dimensional Heisenberg antiferromagnets near quantum criticality using quantum Monte Carlo simulations, revealing a consistent renormalized relationship across different regimes.

Contribution

It demonstrates that a single-layer mean-field theory with a renormalized coordination number applies across multiple quantum regimes, extending previous understanding of Neel temperature scaling.

Findings

The relationship hi_s^{2D}(T_N)=(z_2J')^{-1} holds in various regimes with a nearly constant renormalization factor.

The renormalized coordination number z_2 is approximately 0.65-0.70 across regimes.

Universal scaling functions are identified and analyzed.

Abstract

We use a quantum Monte Carlo method to calculate the Neel temperature T_N of weakly coupled S=1/2 Heisenberg antiferromagnetic layers consisting of coupled ladders. This system can be tuned to different two-dimensional scaling regimes for T > T_N. In a single-layer mean-field theory, \chi_s^{2D}(T_N)=(z_2J')^{-1}, where \chi_s^{2D} is the exact staggered susceptibility of an isolated layer, J' the inter-layer coupling, and z_2=2 the layer coordination number. With a renormalized z_2, we find that this relationship applies not only in the renormalized-classical regime, as shown previously, but also in the quantum-critical regime and part of the quantum-disordered regime. The renormalization is nearly constant; k_2 ~ 0.65-0.70. We also study other universal scaling functions.