2025/05/29 by Burkard, Ruben, Schneider, Benedikt, Sbierski, Björn
#Computational Physics (physics.comp-ph) #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2505.23699
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 and 1. The expansion coefficients up to 12th order in J/T are precomputed on all possible ~106 graphs embeddable in arbitrary lattices and are provided under https://github.com/bsbierski/Dyn-HTE. This enables calculation of static momentum-resolved susceptibilities for arbitrary site-pairs or wavevectors. We test our results for the S=1/2 Heisenberg chain and on the 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.