Dimer Order with Striped Correlations in the J_1-J_2 Heisenberg Model

TL;DR

This study compares energies of different ordered states in the J1-J2 Heisenberg model, revealing a likely transition from Néel to quantum disordered and then to a 4-sublattice state, with evidence supporting columnar dimer order and striped correlations.

Contribution

It provides a detailed analysis of ground state energies and excitation spectra, supporting the presence of columnar dimer order over plaquette order in the model.

Findings

Smooth transition from Néel to quantum disordered state at J2/J1 ≈ 0.4

First order transition to 4-sublattice magnetic state at J2/J1 ≈ 0.6

Evidence against plaquette phase due to excitation spectrum analysis

Abstract

Ground state energies for plaquette and dimer order in the $J_1-J_2$ square-lattice spin-half Heisenberg model are compared using series expansion methods. We find that these energies are remarkably close to each other at intermediate values of $J_2/J_1$, where the model is believed to have a quantum disordered ground state. They join smoothly with those obtained from the Ising expansions for the 2-sublattice N\'eel-state at $J_2/J_1 \approx 0.4$, suggesting a second order transition from a N\'eel state to a quantum disordered state, whereas they cross the energy for the 4-sublattice ordered state at $J_2/J_1 \approx 0.6$ at a large angle, implying a first order transition to the 4-sublattice magnetic state. The strongest evidence that the plaquette phase is not realized in this model comes from the analysis of the series for the singlet and triplet excitation spectra, which suggest an instability in the plaquette phase. Thus, our study supports the recent work of Kotov et al, which presents a strong picture for columnar dimer order in this model. We also discuss the striped nature of spin correlations in this phase, with substantial resonance all along columns of dimers.