Quantum Phase Transition in an Interacting Fermionic Chain

TL;DR

This paper rigorously investigates the quantum phase transition in one-dimensional interacting fermionic systems, demonstrating the persistence of Luttinger liquid behavior near criticality despite vanishing Fermi velocity.

Contribution

It provides a rigorous proof of the persistence of Luttinger liquid behavior close to the quantum critical point in interacting fermionic chains.

Findings

Luttinger liquid behavior persists near the critical point.

The analysis handles the vanishing Fermi velocity.

Two multiscale analysis methods are employed.

Abstract

We rigorously analyze the quantum phase transition between a metallic and an insulating phase in (non solvable) interacting spin chains or one dimensional fermionic systems. In particular, we prove the persistence of Luttinger liquid behavior in the presence of an interaction even arbitrarily close to the critical point, where the Fermi velocity vanishes and the two Fermi points coalesce. The analysis is based on two different multiscale analysis; the analysis of the first regime provides gain factors which compensate exactly the small divisors due to the vanishing Fermi velocity.