Ground-State Phase Diagrams of the Two-Dimensional Quantum Heisenberg Spin Glass Models

TL;DR

This study explores the ground-state phase diagrams of two-dimensional quantum Heisenberg spin glass models using exact diagonalization, revealing similarities with Ising models and identifying the persistence of spin glass phases under quantum fluctuations.

Contribution

It provides the first detailed phase diagrams of 2D quantum Heisenberg spin glasses, highlighting the effects of randomness and quantum fluctuations on phase boundaries.

Findings

Bond-random model shares phase diagram with Ising spin glass.

Spin glass phase persists in the site-random model, especially in ferro-rich cases.

Néel phase narrows in the ferro-rich site-random model compared to the Ising counterpart.

Abstract

Ground-state properties of the two-dimensional $S=1/2$ random Heisenberg models are investigated by the exact-diagonalization method. The phase diagram of the bond-random model (the $\pm J$ model) is the same as that of the corresponding Ising spin glass model, in spite of quantum fluctuation. In the site-random model, the spin glass phase exists at least in the ferro-rich case. In comparison with the corresponding Ising model, the N\'eel phase of this model becomes much narrower in the ferro-rich case, while it is comparable in the antiferro-rich case. KEYWORDS: quantum spin glass, Heisenberg model, ground-state phase transition, site-random model, exact diagonalization