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

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 \tildeΛare in their ground state while other bosons (with |k|<\tildeΛ) 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 \tildeΛvanishes and no fermionic excitation is present in the system. In this regime the dynamics is described by transversally coupled Tomonaga-Luttinger bosons.