Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

Reboredo, Fernando A.; Kim, Jeongnim

doi:10.1063/1.4861222

Title: Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

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Abstract

A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo, J. Chem. Phys. 136, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. 89, 6316 (1988)]. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric guiding wave functions. In the process we obtain a parallel algorithm that optimizes a small subspace of the many-body Hilbert space to provide maximum overlap with the subspace spanned by the lowest-energy eigenstates of a many-body Hamiltonian. We show in a model system that the partition function is progressively maximized within this subspace. We show that the subspace spanned by the small basis systematically converges towards the subspace spanned by the lowest energy eigenstates. Possible applications of this method for calculating the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can also be used to accelerate the calculation of the ground or excited states with quantum Monte Carlo.

Authors:

Reboredo, Fernando A.; Kim, Jeongnim ^[1]

Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States)

Publication Date:: Fri Feb 21 00:00:00 EST 2014

OSTI Identifier:: 22255091

Resource Type:: Journal Article

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 140; Journal Issue: 7; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY MATRIX; DIFFUSION; EXCITED STATES; GROUND STATES; HAMILTONIANS; HILBERT SPACE; MANY-BODY PROBLEM; MONTE CARLO METHOD; PARTITION FUNCTIONS; THERMODYNAMIC PROPERTIES; WAVE FUNCTIONS

Citation Formats


                    Reboredo, Fernando A., and Kim, Jeongnim. Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases.  United States: N. p., 2014. 
        Web.  doi:10.1063/1.4861222.

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                    Reboredo, Fernando A., & Kim, Jeongnim. Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases.  United States.  https://doi.org/10.1063/1.4861222

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                    Reboredo, Fernando A., and Kim, Jeongnim. 2014.  
        "Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases".  United States.  https://doi.org/10.1063/1.4861222.

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@article{osti_22255091,

  title        = {Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases},

  author       = {Reboredo, Fernando A. and Kim, Jeongnim},

  abstractNote = {A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo, J. Chem. Phys. 136, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. 89, 6316 (1988)]. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric guiding wave functions. In the process we obtain a parallel algorithm that optimizes a small subspace of the many-body Hilbert space to provide maximum overlap with the subspace spanned by the lowest-energy eigenstates of a many-body Hamiltonian. We show in a model system that the partition function is progressively maximized within this subspace. We show that the subspace spanned by the small basis systematically converges towards the subspace spanned by the lowest energy eigenstates. Possible applications of this method for calculating the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can also be used to accelerate the calculation of the ground or excited states with quantum Monte Carlo.},

  doi          = {10.1063/1.4861222},

  url          = {https://www.osti.gov/biblio/22255091},
  journal      = {Journal of Chemical Physics},

  issn         = {0021-9606},

  number       = 7,

  volume       = 140,

  place        = {United States},

  year         = {Fri Feb 21 00:00:00 EST 2014},

  month        = {Fri Feb 21 00:00:00 EST 2014}

}

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