Spin susceptibility of quantum magnets from high to low temperatures

TL;DR

This paper introduces a novel method to compute the magnetic susceptibility of quantum spin systems across all temperatures by extending high temperature series expansions, accurately capturing low-temperature behavior.

Contribution

The authors develop a new approach based on entropy-energy approximation that extends high temperature series to low temperatures, overcoming divergence issues.

Findings

Achieves susceptibility calculations within a few percent of exact results in 1D models.

Successfully applies the method to 2D models, including the kagome lattice.

Provides a unified framework for analyzing spin susceptibilities from high to low temperatures.

Abstract

We present a method to compute the magnetic susceptibility of spin systems at all temperatures in one and two dimensions. It relies on an approximation of the entropy versus energy (microcanonical potential function) on the whole range of energies. The intrinsic constraints on the entropy function and a careful treatment of boundary behaviors allow to extend the standard high temperature series expansions (HTE) towards zero temperature, overcoming the divergence of truncated HTE. This method is benchmarked against two one-dimensional solvable models: the Ising model in longitudinal field and the XY model in a transverse field. With ten terms in the HTE, we find a spin susceptibility within a few \% of the exact results in the whole range of temperature. The method is then applied to two two-dimensional models: the supposed-to-be gapped Heisenberg model and the $J_1$-$J_2$-$J_d$ model on the kagome lattice.