A way to solve BCS-type pairing model

TL;DR

This paper introduces an exact method for solving the BCS-type pairing model by transforming it into a spin-analogy problem, simplifying the computational complexity and aiding quantum simulation and understanding of many-body quantum systems.

Contribution

The paper presents a novel exact solution approach for the BCS-type pairing model via spin-analogy, avoiding approximations and reducing complexity.

Findings

Transforms an exponential problem into a polynomial one

Provides a theoretical basis for quantum simulation of pairing models

Facilitates understanding of many-body quantum theory

Abstract

We propose a way to solve BCS-type pairing model by to exactly solve its spin-analogy in the subspace. The advantages of our method are to avoid to directly deal with the approximate procedure and to transfer an exponentially complicated problem to a polynomial problem. Moreover, it builds the theoretical foundation of quantum simulation of pairing model and can be used to check the precision of quantum simulation. It is also helpful to understand the many-body quantum theory.