Variational description of the dimensional cross-over in the array of coupled one-dimensional conductors

TL;DR

This paper introduces a variational wave function to analyze the electronic properties of coupled one-dimensional conductors, capturing the transition from fermionic to bosonic behavior as interaction strength varies.

Contribution

It develops a variational approach to describe the dimensional crossover in coupled 1D conductors, incorporating Tomonaga-Luttinger bosons and effective Hamiltonian analysis.

Findings

For weak/intermediate interactions, fermion-like excitations exist.

For strong interactions, fermionic excitations vanish, and bosonic dynamics dominate.

The method enables calculation of low-energy Green's functions.

Abstract

Variational wave function is proposed to describe electronic properties of an array of one-dimensional conductors coupled by transverse hopping and interaction. For weak or intermediate in-chain interaction the wave function has the following structure: Tomonaga-Luttinger bosons with momentum higher then some variational quantity \tilde\Lambda are in their ground state while other bosons (with |k|<\tilde\Lambda) form kinks -- fermion-like excitations of the Tomonaga-Luttinger boson field. Nature of the ground state for this quasiparticles can be determined by solving three dimensional effective hamiltonian. Since the anisotropy of the effective hamiltonian is small the use of the mean field theory is justified. For repulsive interaction possible phases are density wave and p-wave superconductivity. Our method allows us to calculate the low-energy part of different electronic Green's functions. In order to do that it is enough to apply standard perturbation theory technique to the effective hamiltonian. When the in-chain interaction is strong \tilde\Lambda vanishes and no fermionic excitation is present in the system. In this regime the dynamics is described by transversally coupled Tomonaga-Luttinger bosons.