Ground-State Phase Diagram of the Two-Dimensional Quantum Heisenberg Mattis Model

TL;DR

This study explores the ground-state phase diagram of the 2D quantum Heisenberg Mattis model, revealing that quantum fluctuations are not crucial in non-frustrated random spin systems, with phase boundaries similar to classical models.

Contribution

The paper provides the first exact diagonalization analysis of the 2D quantum Heisenberg Mattis model, showing the persistence of classical phase boundaries in the quantum regime.

Findings

Néel order persists in the antiferromagnetic region.

Spin glass order increases with ferro-bond concentration.

Quantum fluctuations are not essential in non-frustrated systems.

Abstract

The two-dimensional $S=1/2$ asymmetric Heisenberg Mattis model is investigated with the exact diagonalization of finite clusters. The N\'eel order parameter and the spin glass order parameter can be smoothly extrapolated to the thermodynamic limit in the antiferromagnetic region, as in the pure Heisenberg antiferromagnet. The critical concentration of the N\'eel phase is consistent with that of the two-dimensional Ising Mattis model, and the spin glass order parameter increases monotonously as the ferro-bond concentration increases. These facts suggest that quantum fluctuation does not play an essential role in two-dimensional non-frustrated random spin systems. KEYWORDS: quantum spin system, ground state, randomness, Mattis model, N\'eel order, spin glass order