Adapted continuous unitary transformation to treat systems with quasiparticles of finite lifetime

TL;DR

This paper introduces an improved continuous unitary transformation method to analyze systems with unstable quasiparticles, demonstrated on a spin ladder model showing triplon decay, revealing spectral and resonance features.

Contribution

The paper develops a novel generator for continuous unitary transformations tailored for systems with finite-lifetime quasiparticles, expanding analytical capabilities.

Findings

Spectral density shows resonance behavior of decaying triplons

Low energy spectrum characterized for the spin ladder system

Method effectively captures quasiparticle decay phenomena

Abstract

An improved generator for continuous unitary transformations is introduced to describe systems with unstable quasiparticles. Its general properties are derived and discussed. To illustrate this approach we investigate the asymmetric antiferromagnetic spin-1/2 Heisenberg ladder which allows for spontaneous triplon decay. We present results for the low energy spectrum and the momentum resolved spectral density of this system. In particular, we show the resonance behavior of the decaying triplon explicitly.