The electron lifetime in Luttinger liquids

TL;DR

This paper studies how electron wavepackets lose coherence in one-dimensional Luttinger liquids at finite temperature, revealing an exponential decay of the Green's function and identifying fractionalization as the main decoherence source.

Contribution

It provides a detailed analysis of electron decoherence and lifetime in Luttinger liquids, highlighting the role of fractionalization and temperature dependence, with new insights into quasiparticle behavior.

Findings

Electron Green's function decays exponentially at long times with a lifetime inversely proportional to temperature.

Electron lifetime is short for strong interactions, indicating non-quasiparticle behavior in Luttinger liquids.

Fractionalization is identified as the main source of electron decoherence in both spinful and spinless cases.

Abstract

We investigate the decoherence of the electron wavepacket in purely ballistic one-dimensional systems described through the Luttinger liquid (LL). At a finite temperature $T$ and long times $t$, we show that the electron Green's function for a fixed wavevector close to one Fermi point decays as $\exp(-t/\tau_F)$, as opposed to the power-law behavior occurring at short times, and the emerging electron lifetime obeys $\tau_F^{-1}\propto T$ for spinful as well as spinless electrons. For strong interactions, $(T\tau_F)\ll 1$, reflecting that the electron is not a good Landau quasiparticle in LLs. We justify that fractionalization is the main source of electron decoherence for spinful as well as spinless electrons clarifying the peculiar electron mass renormalization close to the Fermi points. For spinless electrons and weak interactions, our intuition can be enriched through a diagrammatic approach or Fermi Golden rule and through a Johnson-Nyquist noise picture. We stress that the electron lifetime (and the fractional quasiparticles) can be revealed from Aharonov-Bohm experiments or momentum resolved tunneling. We aim to compare the results with those of spin-incoherent and chiral LLs.