Charged and spin-excitation gaps in half-filled strongly correlated electron systems: A rigorous result

TL;DR

This paper proves rigorously that in certain strongly correlated electron models at half-filling, the charged excitation gaps are always larger than the spin excitation gaps, confirming previous numerical findings.

Contribution

It introduces a generalized Lieb's spin-reflection positivity method to establish a rigorous inequality between charge and spin gaps in these models.

Findings

Charged gaps are larger than spin gaps in the models studied.

The result confirms previous variational and density renormalization group findings.

Provides a rigorous mathematical proof for the gap inequality.

Abstract

By exploiting the particle-hole symmetries of the Hubbard model, the periodic Anderson model and the Kondo lattice model at half-filling and applying a generalized version of Lieb's spin-reflection positivity method, we show that the charged gaps of these models are always larger than their spin excitation gaps. This theorem confirms the previous results derived by either the variational approach or the density renormalization group approach.