Variational RVB wave function for the spin-1/2 Heisenberg Model on honeycomb lattice

TL;DR

This paper introduces a variational RVB wave function for the ground state of the spin-1/2 Heisenberg model on the honeycomb lattice, demonstrating improved energy estimates and anisotropic correlations via VMC.

Contribution

It proposes a long-range RVB wave function for the honeycomb lattice Heisenberg model and evaluates its effectiveness using VMC, showing better energy estimates than some traditional methods.

Findings

Ground state energy is lower than Ne9el state energy.

Spin correlations differ along zig-zag and armchair directions.

Quantum fluctuations do not fully destroy magnetic order.

Abstract

In this work, a long-range resonating valence bond state is proposed as a variational wave function for the ground state of the $S=1/2$ antiferromagnetic Heisenberg model on the honeycomb lattice. Employing Variational Monte Carlo (VMC) method, we show that the ground state energy obtained from such RVB wave function, lies well below the energy of the N\'eel state and compares very well to the energies evaluated from spin-wave theory and series expansion method. We also obtain the spin-spin correlation function along zig-zag and armchair directions and find that the two correlations are different, which indicates the anisotropic nature of the system. We compare our results with the square lattice and we show that although the quantum fluctuations on honeycomb lattice are much stronger, but do not completely destroy the magnetic order.