Local Current Algebra for the HK Universality Class

TL;DR

This paper demonstrates that the HK model for doped Mott insulators can be made local in real space using a current algebra approach, addressing previous criticisms and confirming the model's consistency with charge susceptibility.

Contribution

It introduces a local real-space current algebra formulation for the HK model, eliminating non-locality and validating the model's physical predictions.

Findings

Charge susceptibility from the current Hamiltonian matches that from Fermionic fields.

The HK model is shown to be local in real space despite non-local Fermionic representation.

The approach reinforces the utility of current algebras in strongly interacting systems.

Abstract

We show that a Hamiltonian in terms of the local real-space currents obeying an $\mathfrak{su}_1(2)$ affine Lie algebra eliminates the non-locality in the Hatsugai-Kohmoto model for a doped Mott insulator. We establish this local correspondence through the Bjorken-Johnson-Low prescription for anomalous commutators. With this result, we show that the charge susceptibility computed from the current Hamiltonian is identical to that with the elemental Fermionic fields. Consequently, the HK model is local in real space, though not in terms of the Fermionic fields, thereby eliminating the key criticism of this model and reinforcing the utility of current algebras for strong interactions.