Benchmarking the variational reduced density matrix theory in the doubly-occupied configuration interaction space with integrable pairing models

TL;DR

This paper evaluates the effectiveness of variational reduced density matrix theory in modeling integrable pairing Hamiltonians within the doubly-occupied configuration space, demonstrating high accuracy against exact solutions for systems up to 100 particles.

Contribution

It benchmarks the variational RDM theory against exactly solvable Richardson-Gaudin models, showing its high accuracy and limitations with random single-particle energies.

Findings

Exact results for N-representability conditions in small systems.

High accuracy of the variational approach for large systems.

Loss of exactness with random single-particle energies.

Abstract

The variational reduced density matrix theory has been recently applied with great success to models within the truncated doubly-occupied configuration interaction space, which corresponds to the seniority zero subspace. Conservation of the seniority quantum number restricts the Hamiltonians to be based on the SU(2) algebra. Among them there is a whole family of exactly solvable Richardson-Gaudin pairing Hamiltonians. We benchmark the variational theory against two different exactly solvable models, the Richardson-Gaudin-Kitaev and the reduced BCS Hamiltonians. We obtain exact numerical results for the so-called PQGT N-representability conditions in both cases for systems that go from 10 to 100 particles. However, when random single-particle energies as appropriate for small superconducting grains are considered, the exactness is lost but still a high accuracy is obtained.