Self consistent study of the quantum phases in a frustrated antiferromagnet on the bilayer honeycomb lattice

M Arlego,Hao Zhang,C A Lamas

doi:10.1088/1742-6596/568/4/042019

Abstract

We study the frustrated Heisenberg model on the bilayer honeycomb lattice. The ground-state energy and spin gap are calculated, using different bosonic representations at mean field level and numerical calculations, to explore different sectors of the phase diagram. In particular we make use of a bond operator formalism and series expansion calculations to study the extent of dimer inter-layer phase. On the other hand we use the Schwinger boson method and exact diagonalization on small systems to analyze the evolution of on-layer phases. In this case we specifically observe a phase that presents a spin gap and short range Neel correlations that survives even in the presence of non-zero next-nearest-neighbor interaction and inter-layer coupling.

Highlights

The study of the possible disordered ground states on two-dimensional antiferromagnets has received a great interest in the last years
In particular we make use of a bond operator formalism and series expansion calculations to study the extent of dimer inter-layer phase
On the other hand we use the Schwinger boson method and exact diagonalization on small systems to analyze the evolution of on-layer phases

Summary

Introduction

The study of the possible disordered ground states on two-dimensional antiferromagnets has received a great interest in the last years. In order to complement our study, we have performed series expansion (SE) calculations, starting from the limit of isolated dimers connecting spins from both layers via J⊥ Notice that, this kind of expansions remain valid in the same limit that the bond operator approach (i.e. in the limit of strong inter-layer coupling.) To this end we have performed a continuous unitary transformation on the original Hamiltonian, using the flow equation method. This kind of expansions remain valid in the same limit that the bond operator approach (i.e. in the limit of strong inter-layer coupling.) To this end we have performed a continuous unitary transformation on the original Hamiltonian, using the flow equation method This technique allows to obtain perturbatively an effective Hamiltonian that keeps the block diagonal structure of decoupled dimers. Our calculations shows that BO, ED and SE predict the same behavior

Self consistent Schwinger Boson Mean-Field Theory

Conclusions