Critical scales in anisotropic spin systems from functional renormalization

TL;DR

This paper applies a functional renormalization group method to the 2D XXZ spin-1/2 model, successfully capturing phase transitions and critical scales, with some limitations near the isotropic point.

Contribution

It introduces a fRG approach using auxiliary fermions to analyze anisotropic spin systems, accurately reproducing phase transition behavior and critical scales.

Findings

Correctly reproduces the phase transition between planar and axial order.

Quantitatively matches the Ising limit critical temperatures.

Deviations occur near the isotropic point due to the Mermin-Wagner theorem.

Abstract

We apply a recently developed functional renormalization group (fRG) scheme for quantum spin systems to the spin-1/2 antiferromagnetic XXZ model on a two-dimensional square lattice. Based on an auxiliary fermion representation we derive flow equations which allow a resummation of the perturbation series in the spin-spin interactions. Spin susceptibilities are calculated for different values of the anisotropy parameter. The phase transition between planar and axial ordering at the isotropic point is reproduced correctly. The results for the critical scales from the fRG as quantitative measures for the ordering temperatures are in good agreement with the exact solution in the Ising limit. On the easy-plane side, the deviations from critical temperatures obtained with quantum Monte Carlo are larger but still acceptable. However, at the isotropic point the Mermin-Wagner theorem is violated such that a precise description of the behavior in the vicinity of the phase transition is not possible. We discuss possible reasons for these discrepanies.