Confinement-deconfinement transition in two-coupled chains with umklapp scattering

TL;DR

This paper investigates how umklapp scattering influences the transition between confined and deconfined states in two-coupled chains, revealing a critical scattering strength that induces confinement and analyzing the crossover from 1D to coupled chain behavior.

Contribution

The study introduces a renormalization group analysis of umklapp scattering effects on interchain hopping, identifying the critical conditions for confinement-deconfinement transition in coupled chains.

Findings

Critical umklapp scattering value for transition calculated.

Confinement occurs when umklapp exceeds interchain hopping.

Crossover from 1D to coupled chain regime demonstrated.

Abstract

A role of umklapp scattering has been examined for two-coupled chains with both forward and backward scatterings by applying renormalization group method to bosonized Hamiltonian. It has been found that a state with relevant interchain hopping changes into a state with irrelevant (confined) one when the magnitude of umklapp scattering becomes larger than that of interchain hopping. Critical value of umklapp scattering for such a confinement-deconfinement transition is calculated as the function of interchain hopping and intrachain interactions. A crossover from one-dimensional regime into that of coupled chains is also shown with decreasing temperature.