Single Particle Hopping Between Luttinger Liquids: A Spectral Function Approach

TL;DR

This paper investigates how single particle hopping between coupled Luttinger liquids affects their spectral functions, emphasizing the coherence/incoherence transition and its implications for anisotropic strongly correlated metals like cuprates.

Contribution

It introduces a spectral function approach to distinguish coherence regimes in coupled Luttinger liquids, highlighting the incoherent regime at low hopping rates.

Findings

Absence of clear coherence signals in coupled Luttinger liquids.

Existence of an incoherent regime at low interliquid hopping rates.

Relevance to anisotropic strongly correlated materials like cuprates.

Abstract

We present a pedagogical account of our approach to the problem of Luttinger liquids coupled by interliquid single particle hopping. It is shown that the key issue is that of coherence/incoherence of interliquid hopping, and not of relevance/irrelevance in a renormalization group sense. A clear signal of coherence, present in the case of coupled Fermi liquids, is absent for Luttinger liquids, and we argue for the existence of an incoherent regime when the interliquid hopping rate is sufficiently small. The problem is relevant to any sufficiently anisotropic, strongly correlated metal, and in particular to understanding the anomalous c-axis conductivity in the cuprate superconductors, and the physics of the quasi-1D organic conductors.