Generalized algebraic transformations and exactly solvable classical-quantum models

TL;DR

This paper introduces generalized algebraic transformations to derive exact analytical solutions for hybrid classical-quantum models, enabling precise analysis of complex systems combining classical and quantum components.

Contribution

It presents a novel algebraic mapping method that provides exact solutions for hybrid classical-quantum models, expanding analytical tools in this field.

Findings

Exact solutions for models with classical Ising and quantum Heisenberg spins

Analytical results for systems with localized Ising spins and delocalized electrons

New algebraic transformations applicable to various hybrid classical-quantum systems

Abstract

The rigorous approach aimed at providing exact analytical results for hybrid classical-quantum models is elaborated on the grounds of generalized algebraic mapping transformations. This conceptually simple method allows one to obtain novel interesting exact results for the hybrid classical-quantum models, which may for instance describe interacting many-particle systems composed of the classical Ising spins and quantum Heisenberg spins, the localized Ising spins and delocalized electrons, or many other hybrid systems of a mixed classical-quantum nature.