2015/12/16 by Zhendong Li, Garnet Kin-Lic Chan, Garnet Kin‐Lic Chan
Materials Science · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Electron #Hilbert space #Linguistics #Magnetism in coordination complexes #Mathematical physics #Mathematics #Philosophy #Physics #Quantum electrodynamics #Quantum many-body systems #Quantum mechanics #Renormalization #Space (punctuation) #Theoretical physics #cond-mat.str-el #physics.chem-ph
paper · pdf · doi:10.1063/1.4942174
23 pages, 14 figures, The following article has been submitted to The Journal of Chemical Physics
arxiv created 2015/12/16 · openalex publication_date 2016/02/23 · arxiv updated 2016/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction Ansatz, namely, the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the "physical indices" or the coupling rules in the HS-MPS. Alternatively, simply truncating the "virtual dimension" of the HS-MPS leads to a family of size-extensive wave function Ansätze that can be used efficiently in variational calculations. We make formal and numerical comparisons between the HS-MPS, the traditional Fock-space MPS used in DMRG, and traditional CI approximations. The analysis and results shed light on fundamental aspects of the efficient representation of many-electron wavefunctions through the renormalization of many-body states.