Interchain coherence of coupled Luttinger liquids at all orders in perturbation theory

TL;DR

This paper develops a systematic diagrammatic approach to analyze the interchain coherence in coupled Luttinger liquids, revealing enhanced coherence and breakdown of linear-response theory at strong interactions.

Contribution

It introduces a diagrammatic expansion in powers of interchain hopping and determines the scaling behavior of coherence and Fermi surface warp at all orders.

Findings

Higher-order diagrams dominate exponents at strong interactions

Enhanced coherence observed beyond linear-response predictions

Results valid at any finite order in interchain hopping

Abstract

We analyze the problem of Luttinger liquids coupled via a single-particle hopping $\tp$ and introduce a systematic diagrammatic expansion in powers of $\tp$. An analysis of the scaling of the diagrams at each order allows us to determine the power-law behavior versus $\tp$ of the interchain hopping and of the Fermi surface warp. In particular, for strong interactions, we find that the exponents are dominated by higher-order diagrams producing an enhanced coherence and a failure of linear-response theory. Our results are valid at any finite order in $\tp$ for the self-energy.