Hidden unity in the quantum description of matter

TL;DR

This paper presents an algebraic framework for interacting quantum systems that reveals underlying unity among diverse phenomena, establishing universal principles and connections through the use of languages and dictionaries.

Contribution

It introduces a novel algebraic approach that uncovers hidden connections and the universality of physical phenomena in complex quantum matter.

Findings

Unveils hidden unity among diverse quantum phenomena

Establishes exact connections between seemingly unrelated phenomena

Introduces the concept of universality beyond critical behavior

Abstract

We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterized by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity behind seemingly unrelated physical phenomena, thus establishing exact connections between them. This leads to the fundamental concept of {\it universality} of physical phenomena, a general concept not restricted to the domain of critical behavior. Key to our framework is the concept of {\it languages} and the construction of {\it dictionaries} relating them.