The functional integral in the Hubbard model

TL;DR

This paper introduces a novel functional integral approach for the Hubbard model, revealing a regime with a deformed measure linked to Jackson and p-adic integrals, and explores quantum group symmetries in the effective functional.

Contribution

It presents a new functional integral formulation for the Hubbard model, connecting deformed measures to Jackson and p-adic integrals, and uncovers quantum group structures in the effective theory.

Findings

Identification of a regime with a deformed integration measure

Connection to Jackson and p-adic functional integrals

Discovery of quantum SU_{rq}(2) group in the effective functional

Abstract

In a new functional integral approach proposed for the model, we find the regime with a deformed integration measure in which the standard integral is replaced with the Jackson integral. We indicate the relation to a p-adic functional integral. For the magnetic and electronic subsystems in the effective functional that results from the operator formulation of the Hubbard model, we find the two-parametric quantum derivative resulting in the appearance of the quantum SU_{rq}(2) group. We establish the relation to the one-parametric quantum derivative and the standard derivative.