A note on density correlations in the half-filled Hubbard model

TL;DR

This paper proves that density-density correlations in the half-filled 1D Hubbard model decay exponentially, resolving a subtlety not obvious from previous Bethe Ansatz and conformal field theory analyses.

Contribution

It demonstrates how symmetry arguments can complement BA/CFT methods to establish exponential decay of correlations in the model.

Findings

Correlations decay exponentially in the half-filled Hubbard model.

Symmetry arguments can be used alongside BA/CFT to analyze correlations.

The decay behavior aligns with intuitive expectations for the model.

Abstract

We consider density-density correlations in the one-dimensional Hubbard model at half filling. On intuitive grounds one might expect them to exhibit an exponential decay. However, as has been noted recently, this is not obvious from the Bethe Ansatz/conformal field theory (BA/CFT) approach. We show that by supplementing the BA/CFT analysis with simple symmetry arguments one can easily prove that correlations of the lattice density operators decay exponentially.