Localized and propagating excitations in gapped phases of spin systems with bond disorder

TL;DR

This paper investigates how bond disorder affects gapped spin systems across different dimensions, revealing that disorder causes damping and localization of excitations, with significant differences between 1D, 2D, and 3D cases.

Contribution

The study applies a T-matrix approach to analyze the effects of bond disorder on elementary excitations in gapped spin systems across multiple dimensions, highlighting localization phenomena.

Findings

Disorder induces damping of propagating excitations in 2D and 3D systems.

All states become localized in 1D systems due to disorder.

States near the band edges exhibit localization, while those far from edges behave like wavepackets.

Abstract

Using the conventional $T$-matrix approach, we discuss gapped phases in 1D, 2D, and 3D spin systems (both with and without a long range magnetic order) with bond disorder and with weakly interacting bosonic elementary excitations. This work is motivated by recent experimental and theoretical activity in spin-liquid-like systems with disorder and in the disordered interacting boson problem. In particular, we apply our theory to both paramagnetic low-field and fully polarized high-field phases in dimerized spin-$\frac12$ systems and in integer-spin magnets with large single-ion easy-plane anisotropy $\cal D$ with disorder in exchange coupling constants (and/or $\cal D$). The elementary excitation spectrum and the density of states are calculated in the first order in defects concentration $c\ll1$. In 2D and 3D systems, the scattering on defects leads to a finite damping of all propagating excitations in the band except for states lying near its edges. We demonstrate that the analytical approach is inapplicable for states near the band edges and our numerical calculations reveal their localized nature. We find that the damping of propagating excitations can be much more pronounced in considered systems than in magnetically ordered gapless magnets with impurities. In 1D systems, the disorder leads to localization of all states in the band, while those lying far from the band edges (short-wavelength excitations) can look like conventional wavepackets.