The patching of critical points using quantum group

TL;DR

This paper proposes a novel approach to modeling phase transitions in condensed matter systems using quantum group symmetries, patching critical points, and connecting gauge theories with condensed matter phenomena.

Contribution

It introduces a method to patch critical points using quantum group-based gauge theories, linking condensed matter physics with gauge and string theories.

Findings

Identification of fixed points related to quantum parameters

Proposal of ensemble averaging over critical points

Potential connection between Hubbard model and gauge/string theories

Abstract

Following our recent conjecture to model the phenomenona of antiferromagnetism and superconductivity by quantum symmetry groups, we discuss in the present note how to construct a workable scenario using this symmetry. In particular we propose to patch the relevant critical points. This means we identify fixed points, corresponding to various $k$ or $q$ [since the two are related] and make expansion around these points, to control these expansion we can impose gauge structure and we thus arrive at quantum group based gauge theory or collection of classical gauge theories which represent the condensed matter system such as cuprates. This is different than ordinary gauge theories in several ways, for in ordinary field theory one has well-defined critical point here the critical points are not unique or simple. In short the real transition than in condensed matter system is represented by collection or {\it ensemble average} of the several chosen critical points which come from ordinary field theory [gauge theory]. This idea may reveal the connection between Hubbard model and gauge theory and string theory. In short it can lead to the non-perturbative formualtion of Hubbard and other condensed matter Hamiltonians.