Jordan-Wigner Transformation for the Description of Strong Correlation in Fermionic Systems

TL;DR

This paper introduces a method using the Jordan-Wigner transformation to efficiently approximate strongly correlated fermionic systems with DOCI-level accuracy for energies and density matrices, avoiding computational collapse.

Contribution

The work demonstrates that applying the Jordan-Wigner transformation enables polynomial-cost, DOCI-quality results for strongly correlated systems, linking fermionic and seniority zero representations.

Findings

Achieves DOCI-quality energies and density matrices with polynomial cost.

Proves the Hartree-Fock wave function transforms to variational coupled cluster doubles.

Provides accurate results for the Hubbard model and small molecular dissociations.

Abstract

Seniority is a useful way of organizing Hilbert space for strongly correlated systems. The exact zero-seniority wave function, doubly-occupied configuration interaction (DOCI), provides accurate results (given the right orbitals) for many strongly correlated electronic systems but has a combinatorial computational cost. In many cases, pair coupled cluster doubles provides a polynomial-cost approximation that closely reproduces the energies of DOCI, but it breaks down in some cases and, as shown herein, it does not provide particularly good density matrices. In this work, we demonstrate that by using the Jordan-Wigner transformation to turn the seniority zero problem back into a fermionic one, we can provide mean-field variational results of DOCI quality for the Hubbard model and a few small molecular dissociation examples, with polynomial cost, both for the energies and for density matrices, all while being protected from collapse. This success is rooted in the proof we provide showing that the Hartree-Fock wave function on the Jordan-Wigner--transformed Hamiltonian transforms back to variational coupled cluster doubles in the seniority zero representation, but restricted to have determinant rather than permanent amplitude coefficients, without compromising its overall accuracy.