Matrix product states for Hartree-Fock-Bogoliubov wave functions

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.