Partial node configuration-interaction Monte Carlo as applied to the Fermi polaron

M. Kolodrubetz, B. K. Clark

Research output: Contribution to journalArticle

Abstract

Finding the ground state of a fermionic Hamiltonian using quantum Monte Carlo (QMC) is a very difficult problem, due to the Fermi sign problem. While still scaling exponentially, full configuration-interaction Monte Carlo (FCIQMC) mitigates some of the exponential variance by allowing annihilation of noise-whenever two walkers arrive at the same configuration with opposite signs, they are removed from the simulation. While FCIQMC has been quite successful for quantum chemistry problems, its application to problems in condensed systems has been limited. In this paper, we apply the FCIQMC algorithm to the Fermi polaron problem, which provides an ideal test bed for improving the algorithm, although since we restrict the number of many-body excitations, our algorithm is more precisely a QMC implementation of the configuration-interaction method (CIQMC). In its simplest form, CIQMC is unstable for even a fairly small system sizes. However, with a series of algorithmic improvements, we are able to significantly increase its effectiveness. We modify fixed node QMC to work in these systems, introduce a well chosen importance sampled trial wave function, a partial node approximation, and a variant of release node. Finally, we develop a way to perform CIQMC directly in the thermodynamic limit.

Original languageEnglish (US)
Article number075109
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume86
Issue number7
DOIs
StatePublished - Aug 6 2012
Externally publishedYes

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Gene Conversion
configuration interaction
Hamiltonians
Quantum chemistry
test stands
quantum chemistry
Wave functions
Ground state
wave functions
Thermodynamics
scaling
thermodynamics
ground state
configurations
approximation
excitation
simulation

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Partial node configuration-interaction Monte Carlo as applied to the Fermi polaron. / Kolodrubetz, M.; Clark, B. K.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 86, No. 7, 075109, 06.08.2012.

Research output: Contribution to journalArticle

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