Decay of fermionic quasiparticles in one-dimensional quantum liquids

TL;DR

This paper investigates the decay rates of fermionic quasiparticles in one-dimensional quantum liquids, revealing a unique eighth-power energy scaling that differs from bosonic excitations, with implications for experimental measurements.

Contribution

It provides the first detailed calculation of fermionic quasiparticle decay rates and their distinct energy dependence in 1D quantum liquids.

Findings

Fermionic excitations decay rate scales as energy to the eighth power.

Fermionic decay is significantly slower than bosonic decay.

Results are experimentally testable via spectral function broadening.

Abstract

The low-energy properties of one-dimensional quantum liquids are commonly described in terms of the Tomonaga-Luttinger liquid theory, in which the elementary excitations are free bosons. To this approximation the theory can be alternatively recast in terms of free fermions. In both approaches, small perturbations give rise to finite lifetimes of excitations. We evaluate the decay rate of fermionic excitations and show that it scales as the eighth power of energy, in contrast to the much faster decay of bosonic excitations. Our results can be tested experimentally by measuring the broadening of power-law features in the density structure factor or spectral functions.