Magnetic susceptibility of quantum spin systems calculated by sine square deformation: one-dimensional, square lattice, and kagome lattice Heisenberg antiferromagnets

TL;DR

This paper introduces a sine square deformation method that enables efficient and accurate calculation of bulk magnetic susceptibility in quantum spin systems using small system sizes, applicable to various lattice geometries.

Contribution

The authors develop a novel numerical approach using sine square deformation to accurately compute susceptibilities in quantum many-body systems without large-scale simulations.

Findings

The method yields susceptibilities within 10^-3 accuracy for the Heisenberg chain and square lattice.

It significantly reduces the required system size for reliable susceptibility estimates.

Applied to kagome lattice, it facilitates investigation of spin liquid candidates.

Abstract

We develop a simple and unbiased numerical method to obtain the uniform susceptibility of quantum many body systems. When a Hamiltonian is spatially deformed by multiplying it with a sine square function that smoothly decreases from the system center toward the edges, the size-scaling law of the excitation energy is drastically transformed to a rapidly converging one. Then, the local magnetization at the system center becomes nearly size independent; the one obtained for the deformed Hamiltonian of a system length as small as L=10 provides the value obtained for the original uniform Hamiltonian of L=100. This allows us to evaluate a bulk magnetic susceptibility by using the magnetization at the center by existing numerical solvers without any approximation, parameter tuning, or the size-scaling analysis. We demonstrate that the susceptibilities of the spin-1/2 antiferromagnetic Heisenberg chain and square lattice obtained by our scheme at L=10 agree within 10 to (-3) with exact analytical and numerical solutions for L=infinite down to temperature of 0.1 times the coupling constant. We apply this method to the spin-1/2 kagome lattice Heisenberg antiferromagnet which is of prime interest in the search of spin liquids.