Finite energy spectral function of an anisotropic 2D system of coupled Hubbard chains

TL;DR

This paper investigates how weak inter-chain couplings influence the spectral properties of a 2D anisotropic Hubbard model, revealing persistent one-dimensional features and the effects of frustration on spectral characteristics.

Contribution

It provides a detailed analysis of the crossover from 1D to 2D in the Hubbard model using a spin-charge factorized wave function and RPA, highlighting the persistence of 1D features.

Findings

Significant 1D spectral characteristics remain in the 2D system.

Inter-chain hopping induces a transition from Luttinger-liquid to Fermi-liquid behavior.

Frustrating hoppings extend the 1D spectral features in energy and momentum space.

Abstract

We study the crossover from the one-dimensional to the two-dimensional Hubbard model in the photoemission spectra of weakly coupled chains. The chains with on-site repulsion are treated using the spin-charge factorized wave function, that is known to provide an essentially exact description of the chain in the strong coupling limit. The hoppings between the chains are considered as a perturbation. We calculate the dynamical spectral function at all energies in the random-phase approximation, by resuming an infinite set of diagrams. Even though the hoppings drive the system from a fractionalized Luttinger-liquid-like system to a Fermi-liquid-like system at low energies, significant characteristics of the one-dimensional system remain in the two-dimensional system. Furthermore, we find that introducing (frustrating) hoppings beyond the nearest neighbor one, the interference effects increase the energy and momentum range of the one--dimensional character.