AKLT Models with Quantum Spin Glass Ground States

TL;DR

This paper explores AKLT models on various lattices, revealing diverse ground states including quantum paramagnetic, Nél, and quantum vector spin glass states, with implications for understanding frustration and ordering in quantum spin systems.

Contribution

It introduces the study of AKLT models on locally tree-like lattices, identifying new spin glass ground states caused by geometric frustration without randomness in couplings.

Findings

Identification of quantum paramagnetic and valence bond solid ground states.

Discovery of critical and ordered Nél states on Cayley trees.

Observation of quantum vector spin glass states on random graphs.

Abstract

We study AKLT models on locally tree-like lattices of fixed connectivity and find that they exhibit a variety of ground states depending upon the spin, coordination and global (graph) topology. We find a) quantum paramagnetic or valence bond solid ground states, b) critical and ordered N\'eel states on bipartite infinite Cayley trees and c) critical and ordered quantum vector spin glass states on random graphs of fixed connectivity. We argue, in consonance with a previous analysis, that all phases are characterized by gaps to local excitations. The spin glass states we report arise from random long ranged loops which frustrate N\'eel ordering despite the lack of randomness in the coupling strengths.