An Exactly Solvable Model of N Coupled Luttinger Chains

TL;DR

This paper presents an exact solution for a model of N coupled Luttinger chains, revealing how the system transitions from Luttinger liquid behavior to Fermi liquid as the number of chains approaches infinity.

Contribution

It provides an exact analytical calculation of the Green function and anomalous dimension for a solvable model of coupled Luttinger chains with arbitrary interchain hopping.

Findings

Luttinger liquid behavior persists for finite N

Coherent interchain hopping is possible despite Luttinger liquid properties

Anomalous dimension approaches zero as N approaches infinity, indicating a Fermi liquid

Abstract

We calculate the exact Green function of a special model of N coupled Luttinger chains with arbitrary interchain hopping t_{perp}. The model is exactly solvable via bosonization if the interchain interaction does not fall off in the direction perpendicular to the chains. For any finite N we find Luttinger liquid behavior and explicitly calculate the anomalous dimension gamma^(N). However, the Luttinger liquid state does not preclude coherent interchain hopping. We also show that gamma^(N) -> 0 for N -> infinity, so that in the limit of infinitely many chains we obtain a Fermi liquid.