Exact Diagonalization Approach for the infinite D Hubbard Model

TL;DR

This paper introduces an exact diagonalization method for analyzing the infinite-dimensional Hubbard model, providing highly accurate thermodynamic and spectral properties at finite and zero temperatures, surpassing some existing computational techniques.

Contribution

The authors develop a novel exact diagonalization approach for the infinite D Hubbard model, enabling precise calculations of Green's functions and spectral densities at finite and zero temperatures.

Findings

Accurate calculation of Green's functions at finite temperatures.

Zero-temperature solutions closely match exact results, except at very low frequencies.

Numerical results for spectral densities and self-energy in the paramagnetic phase.

Abstract

We present a powerful method for calculating the thermodynamic properties of the Hubbard model in infinite dimensions, using an exact diagonalization of an Anderson model with a finite number of sites. At finite temperatures, the explicit diagonalization of the Anderson Hamiltonian allows the calculation of Green's functions with a resolution far superior to that of Quantum Monte Carlo calculations. At zero temperature, the Lancz\`os method is used and yields the essentially exact zero-temperature solution of the model, except in a region of very small frequencies. Numerical results for the half-filled case in the paramagnetic phase (quasi-particle weight, self-energy, and also real-frequency spectral densities) are presented.