Benchmark of a modified Iterated Perturbation Theory approach on the 3d FCC lattice at strong coupling

TL;DR

This paper introduces IPT-$D$, a modified Iterated Perturbation Theory method for the Hubbard model on a 3D FCC lattice at strong coupling, improving accuracy away from half-filling by ensuring correct double occupancy.

Contribution

The paper proposes a simple modification to IPT that enhances its accuracy at strong coupling and away from half-filling, validated against CTQMC benchmarks.

Findings

IPT-$D$ recovers Fermi liquid behavior away from half-filling.

Benchmark results show good agreement between IPT-$D$ and CTQMC for key physical quantities.

Particle-hole asymmetry remains significant at high coupling.

Abstract

The Dynamical Mean-Field theory (DMFT) approach to the Hubbard model requires a method to solve the problem of a quantum impurity in a bath of non-interacting electrons. Iterated Perturbation Theory (IPT) has proven its effectiveness as a solver in many cases of interest. Based on general principles and on comparisons with an essentially exact Continuous-Time Quantum Monte Carlo (CTQMC) solver, here we show that the standard implementation of IPT fails away from half-filling when the interaction strength is much larger than the bandwidth. We propose a slight modification to the IPT algorithm that replaces one of the equations by the requirement that double occupancy calculated with IPT gives the correct value. We call this method IPT-$D$. We recover the Fermi liquid ground state away from half-filling. The Fermi liquid parameters, density of states, chemical potential, energy and specific heat on the FCC lattice are calculated with both IPT-$D$ and CTQMC as benchmark examples. We also calculated the resistivity and the optical conductivity within IPT-$D$. Particle-hole asymmetry persists even at coupling twice the bandwidth. Several algorithms that speed up the calculations are described in appendices.