Supergroup approach to the Hubbard model

TL;DR

This paper introduces a novel supergroup-based approach to the Hubbard model, revealing hidden algebraic structures and constructing a curved space framework for analyzing spinless fermions with strong interactions.

Contribution

It develops a new supergroup approach, relates Hubbard operators to spinor representations, and constructs a curved space and superalgebra for the Hubbard model.

Findings

Revealed a hidden supergroup structure in the Hubbard model.

Constructed a matrix representation of translation generators leading to curved space.

Evaluated the effective functional for spinless fermions in the large repulsion regime.

Abstract

Based on the revealed hidden supergroup structure, we develop a new approach to the Hubbard model. We reveal a relation of even Hubbard operators to the spinor representation of the generators of the rotation group of four-dimensional spaces. We propose a procedure for constructing a matrix representation of translation generators, yielding a curved space on which dynamic superfields are defined. We construct a new deformed nonlinear superalgebra for the regime of spinless Hubbard model fermions in the case of large on-site repulsion and evaluate the effective functional for spinless fermions.