Recursive algorithm for generating high-temperature expansions for spin systems and the chiral non-linear susceptibility

TL;DR

This paper introduces a recursive algorithm derived from the renormalization group flow to compute high-temperature expansions for quantum spin systems, enabling estimation of critical temperatures and calculation of complex susceptibilities.

Contribution

The paper presents a novel recursive method in closed form for high-temperature expansions of quantum spin systems based on the exact RG flow equation.

Findings

Estimated critical temperatures of Heisenberg magnets.

Calculated chiral non-linear susceptibility up to second order.

Validated the recursive algorithm's effectiveness.

Abstract

We show that the high-temperature expansion of the free energy and arbitrary imaginary-time-ordered connected correlation functions of quantum spin systems can be recursively obtained from the exact renormalization group flow equation for the generating functional of connected spin correlation functions derived by Krieg and Kopietz [Phys. Rev. B 99, 060403(R) (2019)]. Our recursive algorithm can be explicitly written down in closed form including all combinatorial factors. We use our method to estimate critical temperatures of Heisenberg magnets from low-order truncations of the inverse spin susceptibility in the static limit. We also calculate the connected correlation function involving three different spin components (chiral non-linear susceptibility) of quantum Heisenberg magnets up to second order in the exchange couplings.