The Mott-Hubbard Transition on the D=infinity Bethe Lattice

TL;DR

This paper investigates the Mott-Hubbard transition in infinite dimensions using a novel cluster approach, revealing a continuous gap opening at a specific critical interaction strength and developing a low-energy theoretical framework.

Contribution

It introduces an exact mapping of truncated Bethe lattices to finite Hubbard-like clusters and compares numerical self-energy results with self-consistent solutions.

Findings

The Mott gap opens continuously at U_c ≈ 2.5t*

Exact cluster mapping for Bethe lattices of any order

Development of a low-energy theory with critical exponent relations

Abstract

In view of a recent controversy we investigated the Mott-Hubbard transition in D=infinity with a novel cluster approach. i) We show that any truncated Bethe lattice of order n can be mapped exactly to a finite Hubbard-like cluster. ii) We evaluate the self-energy numerically for n=0,1,2 and compare with a series of self-consistent equation-of-motion solutions. iii) We find the gap to open continously at the critical U_c~2.5t* (t = t* / sqrt{4d}). iv) A low-energy theory for the Mott-Hubbard transition is developed and relations between critical exponents are presented.