Energy of the nearest neighbor RVB state by systematic loop expansion

TL;DR

This paper introduces a systematic loop expansion method to approximate the norm and energy of the nearest-neighbor RVB state in the 2D Heisenberg antiferromagnet, providing accurate ground state energy estimates.

Contribution

A novel systematic loop expansion scheme for calculating the norm and energy of the nearest-neighbor RVB state in 2D antiferromagnets.

Findings

Expansion converges well with increasing loop length.

Estimated ground state energy per site is -0.434473J.

Method provides a systematic approach for energy calculations.

Abstract

We present an approximation scheme for the calculation of the norm and energy of the nearest-neighbor-RVB state for the Heisenberg antiferromagnet on the 2D square lattice. The approximation leads to a systematic expansion of norm and energy, with the `expansion parameter' being the maximum length of loops taken into account in the calculation of energy and norm. The expansion converges well, the best estimate for the ground state energy/site is $-0.434473J$.