Breakdown of the Fermi Liquid picture in one dimensional fermion systems: connection with the energy level statistics

TL;DR

This paper explores the breakdown of the Fermi liquid theory in one-dimensional fermion systems, linking the existence of quasiparticles to a specific interaction strength and analyzing energy level statistics for different models.

Contribution

It establishes a condition for quasiparticle existence in Luttinger liquids and connects it to a crossover in energy level statistics from non-interacting to integrable system behavior.

Findings

Interaction strength scales with system size as inverse square root.

Energy level statistics transition from non-interacting to exponential distribution.

Analysis of level statistics in coupled chain models.

Abstract

Using the adiabatic switching of interactions, we establish a condition for the existence of electronic quasiparticles in a Luttinger liquid. It involves a characteristic interaction strength proportional to the inverse square root of the system length. An investigation of the exact energy level separation probability distribution shows that this interaction scale also corresponds to a cross-over from the non interacting behaviour to a rather typical case for integrable systems, namely an exponential distribution. The level spacing statistics of a spin $1/2$, one branch Luttinger model are also analyzed, as well as the level statistics of a two coupled chain model.