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

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.

10 pages, 7 figures

References in corpus (4)

• Spin and charge dynamics of the one-dimensional extended Hubbard model
• Properties of the one-dimensional Hubbard model: cellular dynamical mean-field description
• Single particle properties of the 2D Hubbard model for real frequencies at weak coupling: Breakdown of the Dyson series for partial self-energy expansions
• Time-dependent exchange-correlation potential in lieu of self-energy

Cited by in corpus (3)

• Time-dependent exchange-correlation hole and potential of the electron gas
• Dynamical exchange-correlation potential formalism for spin-$\frac{1}{2}$ Heisenberg and Hubbard chains: the antiferromagnetic/half-filled case
• Kondo spectral functions at low-temperatures: A dynamical-exchange-correlation-field perspective