Triplon mean-field analysis of an antiferromagnet with degenerate Shastry-Sutherland ground states

TL;DR

This paper investigates the quantum phase diagram of a spin-1/2 antiferromagnet with degenerate ground states using triplon mean-field theory, revealing stable spin-gapped phases and various magnetic orders.

Contribution

It extends the analysis of a degenerate Shastry-Sutherland antiferromagnet to the thermodynamic limit and identifies new stable phases and phase transitions.

Findings

Discovery of a stable plaquette spin-gapped phase.

Identification of a sublattice columnar dimer phase stabilized by further neighbor interactions.

Observation of level-crossing and continuous phase transitions between phases.

Abstract

We look into the quantum phase diagram of a spin-$\frac{1}{2}$ antiferromagnet on the square lattice with degenerate Shastry-Sutherland ground states, for which only a schematic phase diagram is known so far. Many exotic phases were proposed in the schematic phase diagram by the use of exact diagonalization on very small system sizes. In our present work, an important extension of this antiferromagnet is introduced and investigated in the thermodynamic limit using triplon mean-field theory. Remarkably, this antiferromagnet shows a stable plaquette spin-gapped phase like the original Shastry-Sutherland antiferromagnet, although both of these antiferromagnets differ in the Hamiltonian construction and ground state degeneracy. We propose a sublattice columnar dimer phase which is stabilized by the second and third neighbor antiferromagnetic Heisenberg exchange interactions. There are also some commensurate and incommensurate magnetically ordered phases, and other spin-gapped phases which find their places in the quantum phase diagram. Mean-field results suggest that there is always a level-crossing phase transition between two spin gapped phases, whereas in other situations, either a level-crossing or a continuous phase transition happens.