Variational Wavefunction for Quantum Antiferromagnets

TL;DR

This paper introduces a new variational wavefunction for quantum antiferromagnets that accurately captures long-range correlations and the qualitative differences between integer and half-integer spins, with high overlap to exact ground states.

Contribution

A novel variational wavefunction based on spin-wave expansion that accurately models quantum antiferromagnets and their correlation functions.

Findings

Successfully reproduces long-distance correlation functions in 1D antiferromagnets.

Explains qualitative differences between integer and half-integer spin systems.

Achieves over 99% overlap with exact ground states in 2D XY model for small clusters.

Abstract

We present here a new approach to determine an accurate variational wavefunction for general quantum antiferromagnets, completely defined by the requirement to reproduce the simple and well known spin-wave expansion. By this wavefunction, it is possible to obtain the correct behavior of the long distance correlation functions for the one dimensional $S=1/2$ antiferromagnet, i.e. {\em a system without long range order}. The qualitative difference between the integer and half integer case is also easily understood with this variational approach. Finally we present numerical results for the 2D XY model, showing that the present wavefunction has an overlap $> 0.99 $ to the exact ground state of the $S=1/2$ model for finite system up to $6 \times 6$ clusters.