Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Density matrix renormalisation group Lagrangians.

Garnet Kin-Lic Chan1

  • 1Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA. gc238@cornell.edu

Physical Chemistry Chemical Physics : PCCP
|June 7, 2008
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Coupled Lindblad Pseudomode Theory for Simulating Open Quantum Systems.

Physical review letters·2026
Same author

Predictive free energy simulations through hierarchical distillation of quantum Hamiltonians.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Accurate Crystal Field Hamiltonians of Single-Ion Magnets at Mean-Field Cost.

The journal of physical chemistry letters·2025
Same author

Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States.

Physical review letters·2025
Same author

Quantum many-body linear algebra, Hamiltonian moments, and a coupled-cluster inspired framework.

The Journal of chemical physics·2025
Same author

A 54.6 GHz Clock Transition in Ho<sup>3+</sup> Electron Spin Qubits Assembled into a Metal-Organic Framework.

Journal of the American Chemical Society·2025
Same journal

Grammatical evolution-based design of nucleotic analogs for SARS-CoV-2's replication-transcription complex.

Physical chemistry chemical physics : PCCP·2026
Same journal

Optical frequency comb Fourier transform spectroscopy of the CH<sub>2</sub><sup>79</sup>Br<sup>81</sup>Br, CH<sub>2</sub><sup>79</sup>Br<sub>2</sub>, and CH<sub>2</sub><sup>81</sup>Br<sub>2</sub> isotopologues in the 1180-1210 cm<sup>-1</sup> region.

Physical chemistry chemical physics : PCCP·2026
Same journal

First-principles modeling of polysilazane-derived SiCNH ceramics: insights into the organization of the free-carbon phase.

Physical chemistry chemical physics : PCCP·2026
Same journal

Determining the binding strength of phenolic anchoring groups on hydrated WO<sub>3</sub> surfaces.

Physical chemistry chemical physics : PCCP·2026
Same journal

Activation of methane by the tantalum trioxide anion, TaO<sub>3</sub><sup></sup>.

Physical chemistry chemical physics : PCCP·2026
Same journal

Temperature-dependent recombination dynamics in BH/ZnBr<sub>2</sub> Co-doped CsPbI<sub>3</sub> thin films.

Physical chemistry chemical physics : PCCP·2026
See all related articles

We developed a Lagrangian formulation for the density matrix renormalization group (DMRG). This method variationally finds the optimal DMRG wavefunction, offering analogies to Hartree-Fock theory and enabling analytic response theories.

Area of Science:

  • Quantum Many-Body Physics
  • Computational Chemistry

Background:

  • The density matrix renormalization group (DMRG) is a powerful algorithm for studying one-dimensional quantum systems.
  • Variational methods are crucial for approximating the ground state wavefunction in quantum mechanics.

Purpose of the Study:

  • To introduce a novel Lagrangian formulation for the density matrix renormalization group (DMRG).
  • To derive Lagrangians that yield optimal DMRG wavefunctions variationally.
  • To explore analogies with existing quantum chemistry methods like Hartree-Fock theory.

Main Methods:

  • Developed Lagrangians for the density matrix renormalization group (DMRG).
  • Applied minimization techniques to find optimal wavefunctions within the matrix product ansatz.
  • Investigated the canonical form of the matrix product within the DMRG sweep algorithm.

Related Experiment Videos

Main Results:

  • Introduced Lagrangians that, upon minimization, provide the optimal DMRG wavefunction variationally.
  • Demonstrated that some results align with elementary expressions found in Hartree-Fock theory.
  • Established analogies between the Lagrangian formulation of DMRG and Hartree-Fock theory.

Conclusions:

  • The proposed Lagrangian formulation offers a new perspective on the density matrix renormalization group (DMRG).
  • These Lagrangians are valuable for developing theories of analytic response and derivatives within DMRG.
  • The connection to Hartree-Fock theory provides potential for cross-disciplinary insights.