Plaquette Order in the J1-J2-J3 model: a series expansion analysis

TL;DR

This study uses series expansion via the flow equation method to analyze the stability and extent of the plaquette phase in the two-dimensional J1-J2-J3 antiferromagnetic model, confirming its existence and mapping its phase boundaries.

Contribution

It provides a detailed series expansion analysis of the plaquette phase in the J1-J2-J3 model, extending previous predictions and estimating phase boundaries.

Findings

The plaquette phase remains stable over a wide range of couplings.

The phase connects adiabatically to the J1-J2-J3 model but not to the J1-J2 model at J3=0.

Critical lines are estimated using Dlog-Pade analysis.

Abstract

Series expansion based on the flow equation method is employed to study the zero temperature properties of the spin-1/2 J1-J2-J3 antiferromagnet in two dimensions. Starting from the exact limit of decoupled plaquettes in a particular generalized J1-J2-J3 model we analyze the evolution of the ground state energy and the elementary triplet excitations in powers of all three inter-plaquette couplings up to fifth order. We find the plaquette phase to remain stable over a wide range of exchange couplings and to connect adiabatically up to the case of the plain J1-J2-J3 model, however not to the J1-J2 model at J3=0. Besides confirming the existence of such a phase, recently predicted by Mambrini, et al. [Phys. Rev. B 74, 144422 [2006)], we estimate its extent by Dlog-Pade analysis of the critical lines that result from closure of the triplet gap.