Two quantum spin models on the checkerboard lattice with an exact two-fold degenerate Shastry-Sutherland ground state

TL;DR

This paper constructs and analyzes two quantum spin models on the checkerboard lattice, demonstrating exact ground states with two-fold degeneracy and exploring phase diagrams and exact solutions for ladder variants.

Contribution

It introduces two specific quantum spin models with exact degenerate ground states and provides conditions for ferromagnetic phases, along with approximate phase diagrams and exact ladder solutions.

Findings

Ground states are two-fold degenerate Shastry-Sutherland singlets.

Exact conditions for ferromagnetic ground states are derived.

A ladder model exhibits exact level-crossing between rung-singlet and AKLT states.

Abstract

Two quantum spin models with bilinear-biquadratic exchange interactions are constructed on the checkerboard lattice. It is proved that, under certain sufficient conditions on the exchange parameters, their ground states consist of two degenerate Shastry-Sutherland singlet configurations. The constructions are studied for arbitrary spin-S. The sufficient conditions for the existence of ferromagnetic ground state are also found exactly. The approximate quantum phase diagrams are presented using the exact results, together with a variational estimate for the N\'eel antiferromagnetic phase. A two-leg spin-1/2 ladder model, based on one of the above constructions, is considered which admits exact solution for a large number of eigenstates. The ladder model is shown to have exact level-crossing between the rung-singlet state and the AKLT state in the singlet ground state. Also introduced is the notion of perpendicularity for quantum spin vectors, which appears in the discussion on one of the two checkerboard models, and is discussed in the Appendix.