Matrix product states for Hartree-Fock-Bogoliubov wave functions

TL;DR

This paper introduces an efficient method to convert Hartree-Fock-Bogoliubov wave functions into matrix product states, enabling better application of these wave functions in quantum many-body problems.

Contribution

The authors develop a novel explicit formula for MPS approximation of Bogoliubov vacua, leveraging their unique entanglement structure.

Findings

Method accurately converts HFB wave functions to MPS

Benchmarking shows high performance on Kitaev chain and honeycomb lattice models

Facilitates combining HFB wave functions with DMRG techniques

Abstract

We provide an efficient and accurate method for converting Hartree-Fock-Bogoliubov wave functions into matrix product states (MPSs). These wave functions, also known as Bogoliubov vacua, exhibit a peculiar entanglement structure that the eigenvectors of the reduced density matrix are also Bogoliubov vacua. We exploit this important feature to obtain their optimal MPS approximation and derive an explicit formula for corresponding MPS matrices. The performance of our method is benchmarked with the Kitaev chain and the Majorana-Hubbard model on the honeycomb lattice. The approach facilitates the applications of Hartree-Fock-Bogoliubov wave functions and is ideally suited for combining with the density-matrix renormalization group method.