title: Hilbert space renormalization for the many-electron problem.
abstract: 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.
authors.affiliation: Department of Chemistry, Frick Laboratory, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Zhendong
authors.initials: Z
authors.lastname: Li
authors.affiliation: Department of Chemistry, Frick Laboratory, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Garnet Kin-Lic
authors.initials: GK
authors.lastname: Chan