Duality, Quantum Skyrmions and the Stability of an SO(3) Two-Dimensional Quantum Spin-Glass

TL;DR

This paper investigates quantum skyrmions in a disordered 2D SO(3) quantum spin system, revealing their gapless nature in the spin-glass phase and proposing a symmetric characterization of this phase.

Contribution

It introduces a duality framework for analyzing quantum skyrmions in disordered 2D magnetic systems and characterizes the spin-glass phase through topological and spin excitation parameters.

Findings

Skyrmion correlators decay as a power law in the spin-glass phase.

The spin-glass phase is gapless and dual to the antiferromagnetic phase.

The phase diagram is consistent with the Berezinskii-Kosterlitz-Thouless mechanism.

Abstract

Quantum topological excitations (skyrmions) are analyzed from the point of view of their duality to spin excitations in the different phases of a disordered two-dimensional, short-range interacting, SO(3) quantum magnetic system of Heisenberg type. The phase diagram displays all the phases, which are allowed by the duality relation. We study the large distance behavior of the two-point correlation function of quantum skyrmions in each of these phases and, out of this, extract information about the energy spectrum and non-triviality of these excitations. The skyrmion correlators present a power-law decay in the spin-glass(SG)-phase, indicating that these quantum topological excitations are gapless but nontrivial in this phase. The SG phase is dual to the AF phase, in the sense that topological and spin excitations are respectively gapless in each of them. The Berezinskii-Kosterlitz-Thouless mechanism guarantees the survival of the SG phase at $T \neq 0$, whereas the AF phase is washed out to T=0 by the quantum fluctuations. Our results suggest a new, more symmetric way of characterizing a SG-phase: one for which both the order and disorder parameters vanish, namely $<\sigma > = 0 $, $<\mu > =0 $, where $\sigma$ is the spin and $\mu$ is the topological excitation operators.