Scaling Regimes, Crossovers, and Lattice Corrections in 2D Heisenberg Antiferromagnets

TL;DR

This study investigates the scaling behavior and crossover phenomena in 2D Heisenberg antiferromagnets with different spins, revealing temperature-dependent velocities and regimes consistent with universal scaling functions and quantum critical predictions.

Contribution

It provides detailed analysis of scaling regimes, spin-wave velocities, and crossovers in 2D Heisenberg antiferromagnets, including S=1/2 and S=1 models, using high temperature expansions and comparisons with sigma-model predictions.

Findings

Spin-wave velocity c is temperature dependent, approaching known T=0 value at low T.

Below T0, S=1 model is in the renormalized classical regime.

S=1/2 model exhibits a crossover from RC to QC regime at T=0.55J.

Abstract

We study scaling behavior in 2D, S=1/2 and S=1 Heisenberg antiferromagnets using the data on full q-dependences of the equal time structure factor and the static susceptibility, calculated through high temperature expansions. We also carry out comparisons with a model of two coupled S=1/2 planes with the interlayer coupling tuned to the T=0 critical point. We separately determine the spin-wave velocity c and mass $m=c/\xi$, in addition to the correlation length, $\xi$, and find that c is temperature dependent; only for $T\alt JS$, it approaches its known T=0 value $c_0$. Despite this temperature dependent spin-wave velocity, full q- and $\omega$-dependences of the dynamical susceptibility $\chi(\bf q,\omega)$ agree with the universal scaling functions computable for the $\sigma$-model, for temperatures upto $T_0 \sim 0.6c_0/a$. Detailed comparisons show that below $T_0$ the S=1 model is in the renormalized classical (RC) regime, the two plane model is in the quantum critical (QC) regime, and the S=1/2 model exhibits a RC-QC crossover, centered at T=0.55J. In particular, for the S=1/2 model above this crossover and for the two-plane model at all T, the spin-wave mass is in excellent agreement with the universal QC prediction, $m\simeq 1.04\,T$. In contrast, for the S=1/2 model below the RC-QC crossover, and for the S=1 model at all T, the behavior agrees with the known RC expression. For all models nonuniversal behavior occurs above $T\sim 0.6c_0/a$. Our results strongly support the conjecture of Chubukov and Sachdev that the S=1/2 model is close to the T=0 critical point to exhibit QC behavior.