Spin functional renormalization group for the $J_{1}J_{2}J_{3}$ quantum Heisenberg model

TL;DR

This paper applies a functional renormalization group approach to study the phase diagram of the frustrated $J_{1}J_{2}J_{3}$ quantum Heisenberg model on a cubic lattice, estimating critical temperatures with high accuracy.

Contribution

It introduces a simplified FRG truncation for quantum spin systems that accurately estimates critical temperatures and reveals fixed points in the phase diagram.

Findings

Critical temperature estimates are within 4% of accepted values.

The simplified FRG approach matches the accuracy of more complex methods.

The approach identifies renormalization group fixed points in the phase diagram.

Abstract

We use our recently developed functional renormalization group (FRG) approach for quantum spin systems to investigate the phase diagram of the frustrated $J_{1}J_{2}J_{3}$ quantum Heisenberg model on a cubic lattice. From a simple truncation of the hierarchy of FRG flow equations for the irreducible spin-vertices which retains only static spin fluctuations and neglects the flow of the four-spin interaction, we can estimate the critical temperature with a similar accuracy as the numerically more expensive pseudofermion FRG. In the regime where the ground state exhibits either ferromagnetic or antiferromagnetic order, a more sophisticated truncation including the renormalization of the four-spin interaction as well as dynamic spin fluctuations reveals the underlying renormalization group fixed point and yields critical temperatures which deviate from the accepted values by at most 4 %.