Exact ground state on the 3D analogue of the Shastry-Sutherland model

TL;DR

This paper introduces a three-dimensional analogue of the Shastry-Sutherland model, demonstrating that its dimer singlet ground state remains exactly solvable and stable in 3D, providing insights into quantum frustration and topological phases.

Contribution

The work constructs a 3D version of the SS model with an exactly solvable ground state, extending the understanding of frustration and solvability into higher dimensions.

Findings

Exact dimer singlet ground state persists in 3D

Classical phase diagrams closely follow 2D counterparts

Quantum singlet phase is more robust in 3D

Abstract

Exact results in frustrated quantum many-body systems are rare, especially in dimensions higher than one. The Shastry-Sutherland (SS) model stands out as a rare example of a two-dimensional spin system with an exactly solvable dimer singlet ground state. In this work, we introduce a three-dimensional analogue of the SS lattice, constructed by deforming the pyrochlore lattice to preserve the local SS geometry. Despite the dimensional increase and altered topology, the ground-state phase diagrams of classical Ising and Heisenberg spins, remain analytically tractable and closely follow their 2D counterparts, including the existence of a 1/3 magnetization plateau and umbrella states. Most notably, for quantum spins S = 1/2, the dimer singlet state survives as an exact ground state over a finite region of the phase diagram. We argue, using exact diagonalization, that the singlet phase is stabilized beyond its 2D counterpart, suggesting enhanced robustness in three dimensions. These results offer a rare, controlled platform to explore the impact of dimensionality on quantum frustration, exact solvability, and potential spin liquid behavior in 3D, with relevance to emergent topological and magnetic phases.