Frustrated spin models on two- and three-dimensional decorated lattices with high residual entropy

TL;DR

This paper investigates highly degenerate ground states in frustrated spin models on decorated lattices, revealing high residual entropy and potential applications in quantum cooling and thermal machines.

Contribution

It introduces a mapping of the ground state degeneracy to a site percolation problem, enabling calculation of residual entropy for various lattices, and explores the thermodynamics of these highly degenerate systems.

Findings

Residual entropy exceeds 60% of ln(2) across studied lattices.

Ground-state degeneracy is mapped to a percolation problem on the Lieb lattice.

Low-temperature thermodynamics dominated by exponentially many gapped excitations.

Abstract

We study the ground-state properties of a family of frustrated spin-1/2 Heisenberg models on two- and three-dimensional decorated lattices composed of connected star-shaped units. Each star is built from edge-sharing triangles with an antiferromagnetic interaction on the shared side and ferromagnetic interactions on the others. At a critical coupling ratio, the ideal star model - defined by equal ferromagnetic interactions - exhibits a macroscopically degenerate ground state, which we map onto a site percolation problem on the Lieb lattice. This mapping enables the calculation of exponential ground-state degeneracy and the corresponding residual entropy for square, triangular, honeycomb, and cubic lattices. Remarkably, the residual entropy remains high for all studied lattices, exceeding 60\% of the maximal value ln(2). Despite a gapless quadratic one-magnon spectrum, the low-temperature thermodynamics is governed by exponentially numerous gapped excitations. For a distorted-star variant of the model, the ground-state manifold is equivalent to that of decoupled ferromagnetic clusters, leading to exponential degeneracy with a lower, yet still substantial, residual entropy. At low temperature the system mimics a paramagnetic crystal of non-interacting spins with high spin value ($s=4$ for a square lattice). The obtained results establish a structural design principle for engineering quantum magnets with a high ground-state degeneracy, suggesting promising candidates for enhanced magnetocaloric cooling and quantum thermal machines.