Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice

TL;DR

This study investigates the ground state of the frustrated J1-J2-J3 Heisenberg model on the square lattice, providing evidence for a plaquette valence bond solid phase in a magnetically disordered region using exact diagonalization methods.

Contribution

It demonstrates the presence of a plaquette valence bond solid phase in the J1-J2-J3 model, combining exact diagonalization with valence bond basis analysis to identify the disordered phase.

Findings

Evidence for a magnetically disordered region along (J2+J3)/J1=1/2

Identification of plaquette valence bond solid order in part of the disordered region

Strong agreement between exact diagonalization and valence bond basis results

Abstract

Using both exact diagonalizations and diagonalizations in a subset of short-range valence bond singlets, we address the nature of the groundstate of the Heisenberg spin-1/2 antiferromagnet on the square lattice with competing next-nearest and next-next-nearest neighbor antiferromagnetic couplings (J1-J2-J3 model). A detailed comparison of the two approaches reveals a region along the line (J2+J3)/J1=1/2, where the description in terms of nearest-neighbor singlet coverings is excellent, therefore providing evidence for a magnetically disordered region. Furthermore a careful analysis of dimer-dimer correlation functions, dimer structure factors and plaquette-plaquette correlation functions provides striking evidence for the presence of a plaquette valence bond solid order in part of the magnetically disordered region.