Magnetic and Dynamic Properties of the Hubbard Model in Infinite Dimensions

TL;DR

This paper provides an essentially exact solution for the infinite dimensional Hubbard model using a self-consistent mapping to an impurity model and quantum Monte Carlo, revealing magnetic, pseudogap, and doping effects.

Contribution

It introduces a precise method to solve the infinite dimensional Hubbard model and explores its magnetic and electronic properties with new insights.

Findings

Antiferromagnetism and pseudogap observed at large Coulomb interactions.

Doping suppresses antiferromagnetism and induces a heavy electron metallic state.

Phase boundary at half filling matches three-dimensional Hubbard model results.

Abstract

An essentially exact solution of the infinite dimensional Hubbard model is made possible by using a self-consistent mapping of the Hubbard model in this limit to an effective single impurity Anderson model. Solving the latter with quantum Monte Carlo procedures enables us to obtain exact results for the one and two-particle properties of the infinite dimensional Hubbard model. In particular we find antiferromagnetism and a pseudogap in the single-particle density of states for sufficiently large values of the intrasite Coulomb interaction at half filling. Both the antiferromagnetic phase and the insulating phase above the N\'eel temperature are found to be quickly suppressed on doping. The latter is replaced by a heavy electron metal with a quasiparticle mass strongly dependent on doping as soon as $n<1$. At half filling the antiferromagnetic phase boundary agrees surprisingly well in shape and order of magnitude with results for the three dimensional Hubbard model.