Solving Dynamical Mean-Field Theory at very low temperature using Lanczos Exact Diagonalization

TL;DR

This paper introduces an improved Lanczos-based method for solving impurity Hamiltonians in Dynamical Mean-Field Theory at low temperatures, achieving high accuracy and reduced computational cost.

Contribution

It extends the Lanczos algorithm to include excited states, enabling efficient and accurate finite-temperature solutions in DMFT.

Findings

Achieves high accuracy from T=0 to near the Mott transition temperature.

Substantially reduces computational effort for finite-temperature calculations.

Successfully tested on the Hubbard model.

Abstract

We present an efficient method to solve the impurity Hamiltonians involved in Dynamical Mean-Field Theory at low but finite temperature, based on the extension of the Lanczos algorithm from ground state properties alone to excited states. We test the approach on the prototypical Hubbard model and find extremely accurate results from T=0 up to relatively high temperatures, up to the scale of the critical temperature for the Mott transition. The algorithm substantially decreases the computational effort involved in finite temperature calculations.