### 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 language | English (US) |
---|---|

Article number | 075109 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 86 |

Issue number | 7 |

DOIs | |

State | Published - Aug 6 2012 |

Externally published | Yes |

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### 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.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 86, no. 7, 075109. https://doi.org/10.1103/PhysRevB.86.075109

}

TY - JOUR

T1 - Partial node configuration-interaction Monte Carlo as applied to the Fermi polaron

AU - Kolodrubetz, M.

AU - Clark, B. K.

PY - 2012/8/6

Y1 - 2012/8/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84865084739&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865084739&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.86.075109

DO - 10.1103/PhysRevB.86.075109

M3 - Article

AN - SCOPUS:84865084739

VL - 86

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 7

M1 - 075109

ER -