Spectral Functions of 1D Hubbard Rings with Varying Boundary Conditions

TL;DR

This study investigates how changing boundary conditions affects the spectral functions of finite 1D Hubbard rings, revealing finite-size signatures of spin-charge separation through numerical and analytical methods.

Contribution

It introduces a detailed analysis of boundary condition effects on spectral functions, demonstrating finite-size signatures of spin-charge separation in 1D Hubbard models.

Findings

Identification of spinon and holon features in spectra

Cusps in the spinon band due to twisted boundary conditions

Spectral building principle accurately describes finite-size spectra

Abstract

We study the effect of varying the boundary condition on the spectral function of a finite 1D Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe Ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low energy holon band and its shadow---which span the whole Brillouin zone---and a spinon band present for momenta less than the Fermi momentum. New features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.