Spectral functions of the half-filled 1D Hubbard chain within the exchange-correlation potential formalism

TL;DR

This paper calculates spectral functions of the 1D Hubbard chain using an exchange-correlation potential approach, achieving results that closely match exact solutions and offering insights into the formalism's advantages over traditional methods.

Contribution

It introduces a novel application of the exchange-correlation potential formalism to the 1D Hubbard model, providing analytical spectral functions and comparing them with established numerical results.

Findings

Spectral functions agree well with DMRG results.

Calculated band gap closely matches Bethe ansatz results.

Presented a general solution to the Green function equation of motion.

Abstract

The spectral functions of the one-band half-filled 1D Hubbard chain are calculated using the exchange-correlation potential formalism developed recently. The exchange-correlation potential is adopted from the exact potential derived from the Hubbard dimer. Within an approximation in which the full Green function is replaced by a non-interacting one, the spectral functions can be calculated analytically. Despite the simplicity of the approximation, the resulting spectra are in favorable agreement with the more accurate results obtained from the dynamic density-matrix renormalization group method. In particular, the calculated band gap as a function of $U$ is in close agreement with the exact gap obtained from the Bethe ansatz. In addition, the formal general solution to the equation of motion of the Green function is presented and the difference between the traditional self-energy approach and the exchange-correlation potential formalism is also discussed and elaborated. A simplified Holstein Hamiltonian is considered to further illustrate the general form of the exchange-correlation potential.