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Published February 28, 2016 | Published + Submitted
Journal Article Open

Hilbert space renormalization for the many-electron problem


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.

Additional Information

© 2016 AIP Publishing LLC. Received 15 December 2015; accepted 4 February 2016; published online 23 February 2016. One of the authors (Z.L.) acknowledges helpful discussions with Sheng Guo, Sebastian Wounters, Qiming Sun, and Boxiao Zheng. This work was primarily supported by the US National Science Foundation, through the Award No. NSF CHE-1265277.

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Published - 1_2E4942174.pdf

Submitted - 1512.05218v1.pdf


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August 22, 2023
August 22, 2023