New Evidence for ``Confined Coherence'' in Weakly Coupled Luttinger Liquids

TL;DR

This paper provides new theoretical evidence for a phase called 'confined coherence' in weakly coupled Luttinger liquids, characterized by relevant but incoherent inter-liquid transport within a specific range of the Luttinger liquid exponent.

Contribution

The study introduces the concept of 'confined coherence' and identifies the conditions under which it occurs, based on exact and approximate calculations of interliquid hopping and Green's functions.

Findings

Existence of 'confined coherence' phase in certain Luttinger liquids.

Bound on the Luttinger liquid exponent alpha for this phase.

Discussion of connections with previous research.

Abstract

On the basis of a calculation of the exact interliquid hopping rate and an approximate single particle Green's function, we present new evidence for the existence of a phase of relevant but incoherent inter-Luttinger liquid transport. This phase of ``confined coherence'' occurs when the Luttinger liquid exponent alpha satisfies alpha_c<alpha<1/2. We argue that alpha_c is strictly bounded above by 1/4, and is probably substantially smaller, especially in spin-charge separated Luttinger liquids. We also discuss connections with the work of others.