High-temperature series expansion of the dynamic Matsubara spin correlator

TL;DR

This paper develops a high-temperature series expansion method for the dynamic Matsubara spin correlator in quantum spin models, enabling precise calculations of dynamic susceptibilities and structure factors.

Contribution

The authors extend the high-temperature series expansion to dynamic correlators and provide an algorithm for exact coefficients, applicable to various lattice models.

Findings

Expansion coefficients computed up to 12th order for key models.

Validated results on antiferromagnetic chain and triangular lattice.

Facilitates calculation of real-frequency dynamic structure factors.

Abstract

The high-temperature series expansion for quantum spin models is a well-established tool to compute thermodynamic quantities and equal-time spin correlations, in particular for frustrated interactions. We extend the scope of this expansion to the dynamic Matsubara spin-spin correlator and develop an algorithm that yields exact expansion coefficients in the form of rational numbers. We focus on Heisenberg models with a single coupling constant J and spin lengths S=1/2,1. The expansion coefficients up to 12th order in J/T are precomputed on all possible $\sim 10^6$ graphs embeddable in arbitrary lattices and are provided in a repository. This enables calculation of static momentum-resolved susceptibilities for arbitrary site-pairs or wavevectors. We test our results for the antiferromagnetic S=1/2 chain and triangular lattice model. An important application that we discuss in a companion letter is the calculation of real-frequency dynamic structure factors. This is achieved by identifying the high-frequency expansion coefficients of the Matsubara correlator with frequency moments of the spectral function.