The Mott-Hubbard transition and the paramagnetic insulating state in the two-dimensional Hubbard model

TL;DR

This paper investigates the Mott-Hubbard transition in the two-dimensional Hubbard model, identifying a critical interaction strength that separates metallic and insulating phases, and analyzing the ground state's local magnetic order and electron mobility.

Contribution

It provides analytical evidence for a critical Uc value and characterizes the ground state with local antiferromagnetic order and constrained electron mobility in the insulator.

Findings

Existence of a critical Uc separating metallic and insulating phases

Ground state in the insulator has a small fraction of empty and doubly occupied sites

Electron mobility is constrained by local antiferromagnetic order

Abstract

The Mott-Hubbard transition is studied in the context of the two-dimensional Hubbard model. Analytical calculations show the existence of a critical value Uc of the potential strength which separates a paramagnetic metallic phase from a paramagnetic insulating phase. Calculations of the density of states and double occupancy show that the ground state in the insulating phase contains always a small fraction of empty and doubly occupied sites. The structure of the ground state is studied by considering the probability amplitude of intersite hopping. The results indicate that the ground state of the Mott insulator is characterized by a local antiferromagnetic order; the electrons keep some mobility, but this mobility must be compatible with the local ordering. The vanishing of some intersite probability amplitudes at U=Uc puts a constrain on the electron mobility. It is suggested that such quantities might be taken as the quantities which control the order in the insulating phase.