Instability of the chiral d-wave RVB state for the Heisenberg model on triangular lattice and an improvement of the Gutzwiller approximation

TL;DR

This study uses Variational Monte Carlo to analyze the Heisenberg model on a triangular lattice, revealing the instability of the chiral d-wave RVB state and proposing an improved Gutzwiller approximation for frustrated systems.

Contribution

It demonstrates that the chiral d-wave RVB state is not the true energy minimum and introduces an improved Gutzwiller approximation for better accuracy on frustrated lattices.

Findings

The non-chiral d_{xy} state has lower energy than the chiral d-wave state.

The usual Gutzwiller approximation performs poorly on the triangular lattice.

An improved Gutzwiller approximation yields significantly better results.

Abstract

Through Variational Monte Carlo simulation we show the d-wave RVB pairing in the Heisenberg model on triangular lattice can be better described in terms of a two component order parameter. The fully gapped chiral d-wave RVB state, which is predicted by the mean field theory to be the unique minimum of variational energy in the two dimensional representation space of d-wave pairing, is found to be actually a local maximum and the true minimum of energy is reached by the non-chiral $d_{xy}$ state with line nodes. We also find that the usual Gutzwiller approximation, which enjoys great success for the square lattice system, fails badly on the triangular lattice as a result of the geometric frustration inherent of the system. An improved version of the Gutzwiiler approximation is proposed and is found to give a much better results than the usual one.