Semiclassical picture of the Heisenberg spin glass in two dimensions: from weak localization to hydrodynamics

TL;DR

This paper explores the localization and delocalization of spin-wave excitations in a two-dimensional Heisenberg spin-glass model using a semiclassical approach, revealing how classical order influences quantum excitation behavior and suggesting a path to hydrodynamics.

Contribution

It introduces a semiclassical expansion method to analyze localization properties of spin-wave excitations in 2D Heisenberg spin glasses, linking classical order to quantum dynamics.

Findings

Low-energy excitations around magnetic order are delocalized.

Spin-glass ordered states exhibit weak localization of excitations.

Delocalization persists despite disorder in magnetically ordered states.

Abstract

The two-dimensional Heisenberg spin-glass model is investigated by means of a semiclassical expansion around classical states. At leading order, we obtain an effective quadratic spin-wave Hamiltonian and study the localization properties of its spectrum and eigenfunctions. We find that the nature of the spin-wave excitations, whether they are hydrodynamic or localized modes, depends crucially on the relevance/irrelevance - in the renormalization group sense - of the correlations induced by the underlying classical order in the spin-wave Hamiltonian matrix elements: low-energy excitations around magnetically ordered states are delocalized, whereas those around spin-glass ordered states are localized, albeit weakly. Remarkably, in the magnetically ordered case, spin-wave delocalization is robust with respect to the presence of disorder, even in two spatial dimensions. We interpret this phenomenology by relating the spontaneous breaking of spin-rotation symmetry in the original Heisenberg model to the symmetry and universality class of the resulting quadratic spin-wave Hamiltonian. We conjecture that the hydrodynamic picture can be recovered through the inclusion of interactions among the spin-wave excitations at higher order in the semiclassical expansion, favoring the onset of ergodic behavior.