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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Hilbert space renormalization for the many-electron problem.

Zhendong Li1, Garnet Kin-Lic Chan1

  • 1Department of Chemistry, Frick Laboratory, Princeton University, Princeton, New Jersey 08544, USA.

The Journal of Chemical Physics
|March 3, 2016
PubMed
Summary
This summary is machine-generated.

We introduce Hilbert space renormalization, a new method for describing many-electron correlations. This approach uses Hilbert space matrix product states (HS-MPS) for efficient wavefunction representation in quantum chemistry.

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Area of Science:

  • Quantum Many-Body Physics
  • Computational Quantum Chemistry

Background:

  • Renormalization is a key concept in solving the many-body problem.
  • Density Matrix Renormalization Group (DMRG) and configuration interaction (CI) are established methods.
  • Graphical representations of configuration space are used in quantum chemistry.

Purpose of the Study:

  • Introduce Hilbert space renormalization (HSR) as a novel theoretical tool.
  • Describe and analyze many-electron correlations using HSR.
  • Develop and evaluate the Hilbert space matrix product state (HS-MPS) wavefunction Ansatz.

Main Methods:

  • Renormalization of many-body states within nested Hilbert subspaces.
  • Utilizing the HS-MPS Ansatz for low-rank tensor approximations of configuration interaction spaces.
  • Truncating the virtual dimension of HS-MPS for size-extensive wave function Ansätze.
  • Comparing HS-MPS with Fock-space MPS (used in DMRG) and traditional CI methods.

Main Results:

  • HS-MPS offers a flexible mathematical structure for wavefunction representation.
  • HS-MPS can approximate CI spaces through restricted indices or coupling rules.
  • Truncating HS-MPS virtual dimension yields efficient, size-extensive wave function Ansätze.
  • Formal and numerical comparisons demonstrate the efficacy of HS-MPS.

Conclusions:

  • Hilbert space renormalization provides a new paradigm for classifying and combining configurations.
  • HS-MPS offers an efficient and flexible approach to representing many-electron wavefunctions.
  • The study illuminates fundamental aspects of many-body state renormalization for efficient wavefunction representation.