Direct diagonalization of Fock space for an exact solution of pairing model

TL;DR

This paper presents a method for exactly solving the BCS pairing model by directly diagonalizing Fock space, revealing spectral symmetries and structural features of energy levels.

Contribution

It introduces a novel approach for exact diagonalization of the pairing model and provides formulas and schemes to analyze its energy spectrum.

Findings

Verification of spectral symmetry in Fock subspaces

Identification of common features in energy gaps and bands

Proposed formulas for estimating lowest energy levels

Abstract

We investigate the exact solution of BCS pairing model using direct diagonalization of Fock space. By the data analysis and numerical calculation, we verify the symmetry between energy spectrum of Fock subspaces, obtain the common structure features of energy gaps and energy bands in Hamiltonian spectrum of reduced model, propose the formula to estimate the lowest energy levels in all of the subspaces of reduced model, and suggest a scheme to estimate the respective energy spectrum which can reveal the structure of energy spectrum of pairing model.