Confinement and transverse conductivity in coupled Luttinger liquids

TL;DR

This paper investigates how interchain hopping and transverse conductivity behave in coupled Luttinger liquids, revealing conditions for confinement and incoherent transport, with implications for quasi-1D materials and high-Tc superconductors.

Contribution

It provides numerical evidence on the suppression of inter-chain coherence and the dominance of incoherent transverse conductivity in coupled Luttinger liquids, highlighting the role of the exponent lpha.

Findings

Inter-chain hopping can be suppressed for lpha around 0.4 or smaller.

Transverse conductivity shows a strong incoherent component.

Coherent Drude weight remains small compared to incoherent weight.

Abstract

One--particle interchain hopping in a system of coupled Luttinger liquids is investigated by use of exact diagonalizations techniques. Firstly, the two chains problem of spinless fermions is studied in order to see the behaviour of the band splitting as a function of the exponent $\alpha$ which characterizes the $1D$ Luttinger liquid. Moderate intra-chain interactions can lead to a strong reduction of this splitting. The on-set of the confinement within the individual chains (defined by a vanishing splitting) seems to be governed by $\alpha$. We give numerical evidence that inter-chain coherent hopping can be totally suppressed for $\alpha\sim 0.4$ or even smaller $\alpha$ values. The transverse conductivty is shown to exhibit a strong incoherent part. Even when coherent inter-chain hopping is believed to occur (at small $\alpha$ values), it is shown that the coherent Drude weight is always significantly smaller than the incoherent weight. Implications for the optical experiments in quasi-1D organic or high-$T_c$ superconductors is outlined.