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  • Letter

Matrix product states for Hartree-Fock-Bogoliubov wave functions

Hui-Ke Jin1, Rong-Yang Sun2,3,4, Yi Zhou5,6,2,7,*, and Hong-Hao Tu8,†

  • 1Department of Physics TQM, Technische Universität München, James-Franck-Straße 1, D-85748 Garching, Germany
  • 2Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
  • 3Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS), Kobe, Hyogo 650-0047, Japan
  • 4Quantum Computational Science Research Team, RIKEN Center for Quantum Computing (RQC), Wako, Saitama 351-0198, Japan
  • 5Beijing National Laboratory for Condensed Matter Physics & Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 6Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
  • 7CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
  • 8Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany

  • *yizhou@iphy.ac.cn
  • †hong-hao.tu@tu-dresden.de
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Phys. Rev. B 105, L081101 – Published 1 February, 2022

DOI: https://doi.org/10.1103/PhysRevB.105.L081101

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.

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Phys. Rev. B 105, L081101– Published 1 February, 2022
  • Received 10 December 2021
  • Accepted 21 January 2022
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