Inequalities between ground-state energies of Heisenberg models

TL;DR

This paper investigates the Lieb-Schupp inequality in antiferromagnetic Heisenberg models, analyzing how the energy difference varies across different geometries and its relation to correlation functions, proposing a new conjecture.

Contribution

The study provides numerical analysis of the Lieb-Schupp inequality across various geometries and introduces an empirical relation with correlation function decay.

Findings

Energy difference varies significantly with system geometry.

A correlation between energy difference and correlation decay was empirically observed.

Formulated a conjecture relating energy difference to correlation fall-off.

Abstract

The Lieb-Schupp inequality is the inequality between ground state en- ergies of certain antiferromagnetic Heisenberg spin systems. In our paper, the numerical value of energy difference given by Lieb-Schupp inequality has been tested for spin systems in various geometries: chains, ladders and quasi-two-dimensional lattices. It turned out that this energy difference was strongly dependent on the class of the system. The relation between this difference and a fall-off of a correlation function has been empirically found and formulated as a conjecture.