Suppression of Dimer Correlations in the Two-Dimensional $J_1$-$J_2$ Heisenberg Model: an Exact Diagonalization Study

TL;DR

This study uses exact diagonalization to analyze the ground state of the two-dimensional $J_1$-$J_2$ Heisenberg model, focusing on dimer correlations and translational symmetry breaking, revealing potential spin liquid or weakly dimerized phases.

Contribution

It provides the first detailed exact diagonalization analysis of dimer correlations in the 2D $J_1$-$J_2$ model, highlighting the nature of its ground state.

Findings

Results suggest a homogeneous spin liquid or a weakly dimerized state.

Dimer correlations are small, indicating weak or absent dimer order.

Translational symmetry breaking susceptibility is inconclusive for strong dimerization.

Abstract

We present an exact diagonalization study of the ground state of the spin-half $J_1{-}J_2$ model. Dimer correlation functions and the susceptibility associated to the breaking of the translational invariance are calculated for the $4\times 4$ and the $6\times 6$ clusters. These results -- especially when compared to the one dimensional case, where the occurrence of a dimerized phase for large enough frustration is well established -- suggest either a homogeneous spin liquid or, possibly, a dimerized state with a rather small order parameter.