Correlated valence bond state and its study of the spin-1/2 J1-J2 Anti-ferromagnetic Heisenberg model on a square lattice

TL;DR

This paper introduces correlated valence bond states as a variational wave function for the J1-J2 Heisenberg model, revealing a gapless spin liquid phase in the frustrated regime on a square lattice.

Contribution

It proposes a new class of variational wave functions that handle frustration and negative amplitudes, applied to study the spin liquid phase in the J1-J2 model.

Findings

Paramagnetic phase is a gapless spin liquid across the studied J2/J1 range.

Wave functions effectively describe the system despite the sign problem.

Extensive Monte Carlo sampling confirms the gapless nature of excitations.

Abstract

We propose a class of variational wave functions, namely the correlated valence bond states, for the frustrated Hamiltonian in the paramagnetic phase. This class of wave functions admits negative amplitude and the same sub-lattice pairing when a bipartite lattice is considered, thus suffers from the negative sign problem. However if applied to small systems, the sign problem is manageable using the standard variational Monte Carlo method. We optimize the wave functions for the J1-J2 Anti ferromagnetic Heisenberg model on a square lattice in the coupling region J2/J1 \in [0.45 : 0.56] for system sizes L = 4, 6, 8. To calculate the correlation functions and the order parameters for larger systems, we make the extensive Monte Carlo samplings using the variational parameters optimized at system size L = 8. We find that the paramagnetic phase is a gap-less spin liquid in the entire range of J2/J1 \in [0.45 : 0.56] with a gap-less singlet excitation and a gaped triplet excitation.