New functional representation for Hubbard model, coherent state and tower of algebras

TL;DR

This paper introduces a novel functional representation for strongly interacting systems, featuring a new quantum coherent state and a hierarchical algebraic structure called 'tower of algebras', with implications for metal-insulator transitions.

Contribution

It proposes a new algebraic framework and coherent state for strongly correlated systems, generalizing Gutzwiller approximation and linking deformation parameters to order parameters.

Findings

Introduction of a new functional representation and quantum coherent state.

Development of the 'tower of algebras' hierarchy of models.

Generalization of Gutzwiller approximation for phase transition analysis.

Abstract

New functional representation for the strongly interacting systems is proposed which contains a new type of the quantum coherent state. As a result the new algebraic structure- so called "tower of algebras" appears which gives the tower (or hierarchy) of models. Generalization of Gutzwiller approximation in theory of metal-insulator phase transition is obtained. It is shown that the deformation parameters may be relevant to the order parameters in the physics of strongly correlated systems.