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Related Concept Videos

Dimensionless Groups in Fluid Mechanics01:15

Dimensionless Groups in Fluid Mechanics

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Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...
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Transcorrelated density matrix renormalization group.

Alberto Baiardi1, Markus Reiher1

  • 1ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland.

The Journal of Chemical Physics
|November 3, 2020
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Summary
This summary is machine-generated.

We introduce transcorrelated Density Matrix Renormalization Group (tcDMRG) theory for efficient energy approximation in strongly correlated systems. This method enhances standard DMRG for complex problems beyond quasi-one-dimensional systems.

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Area of Science:

  • Quantum Many-Body Physics
  • Computational Chemistry
  • Condensed Matter Physics

Background:

  • Strongly correlated systems present significant computational challenges for traditional quantum chemistry methods.
  • The Density Matrix Renormalization Group (DMRG) is effective for quasi-one-dimensional systems but struggles with higher dimensions.
  • Accurate energy approximation is crucial for understanding the behavior of these complex materials.

Purpose of the Study:

  • To develop an efficient theoretical framework for approximating the energy of strongly correlated systems.
  • To extend the applicability of DMRG methods to systems beyond quasi-one-dimension.
  • To address the dynamic correlation problem in DMRG calculations.

Main Methods:

  • Introduction of the transcorrelated Density Matrix Renormalization Group (tcDMRG) theory.
  • Encoding the wave function as a product of a Jastrow or Gutzwiller correlator and a matrix product state.
  • Optimization of the matrix product state using the imaginary-time variant of time-dependent DMRG applied to a non-Hermitian transcorrelated Hamiltonian.

Main Results:

  • Demonstrated the efficiency of tcDMRG using the two-dimensional Fermi-Hubbard Hamiltonian.
  • Showcased fast energy convergence across various system sizes, occupation numbers, and interaction strengths.
  • Validated tcDMRG as a powerful approach for dynamic correlation problems.

Conclusions:

  • tcDMRG significantly enhances the efficiency of standard DMRG, particularly for systems beyond quasi-one-dimension.
  • The method provides a generally powerful approach to tackling dynamic correlation problems.
  • tcDMRG offers a promising avenue for accurate energy approximation in complex, strongly correlated systems.