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

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.

Accepted by JCTC

References in corpus (5)

• Quasiparticle Coupled Cluster Theory for Pairing Interactions
• A configuration interaction correction on top of pair coupled cluster doubles
• Robust formulation of Wick's theorem for computing matrix elements between Hartree-Fock-Bogoliubov wavefunctions
• Strong-Weak Duality via Jordan-Wigner Transformation: Using Fermionic Methods for Strongly Correlated $su(2)$ Spin Systems
• Connections between Richardson-Gaudin States, Perfect-Pairing, and Pair Coupled-Cluster Theory

Cited by in corpus (1)

• Seniority-zero Linear Canonical Transformation Theory