From Hubbard to Heisenberg at Half Filling

Abstract: The half-filled repulsive Hubbard model is commonly replaced, in the strong-coupling regime, by an antiferromagnetic Heisenberg model at the superexchange scale (J_0(U)=4t^2/U). This replacement is a standard principle in condensed matter physics, but its justification at the level of canonical Gibbs states requires more than identifying the leading effective Hamiltonian.

In this talk, I will present a quantitative Hubbard-to-Heisenberg comparison for thermodynamic quantities. We compare the canonical pressure densities of the Hubbard model and the corresponding Heisenberg model on finite tori, with an error term for the pressure density that is independent of the system size. The proof combines a strong-coupling Lie--Schwinger/Schrieffer--Wolff diagonalisation with a defect decomposition controlling sectors with empty or doubly occupied sites. As consequences, we obtain staggered-magnetisation comparison in fixed positive fields and suppression of charge defects.

mathematical physics

Audience: researchers in the discipline

One world IAMP mathematical physics seminar

Series comments: In order to receive announcements, please send an email to IAMPseminars@gmail.com with “subscribe” in the subject line.