### Abstract

The sign problem in full configuration interaction quantum Monte Carlo (FCIQMC) without annihilation can be understood as an instability of the psi-particle population to the ground state of the matrix obtained by making all off-diagonal elements of the Hamiltonian negative. Such a matrix, and hence the sign problem, is basis dependent. In this paper, we discuss the properties of a physically important basis choice: first versus second quantization. For a given choice of single-particle orbitals, we identify the conditions under which the fermion sign problem in the second quantized basis of antisymmetric Slater determinants is identical to the sign problem in the first quantized basis of unsymmetrized Hartree products. We also show that, when the two differ, the fermion sign problem is always less severe in the second quantized basis. This supports the idea that FCIQMC, even in the absence of annihilation, improves the sign problem relative to first quantized methods. Finally, we point out some theoretically interesting classes of Hamiltonians where first and second quantized sign problems differ, and others where they do not.

Original language | English (US) |
---|---|

Article number | 024110 |

Journal | Journal of Chemical Physics |

Volume | 138 |

Issue number | 2 |

DOIs | |

State | Published - Jan 14 2013 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*138*(2), [024110]. https://doi.org/10.1063/1.4773819

**The effect of quantization on the full configuration interaction quantum Monte Carlo sign problem.** / Kolodrubetz, M. H.; Spencer, J. S.; Clark, B. K.; Foulkes, W. M C.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 138, no. 2, 024110. https://doi.org/10.1063/1.4773819

}

TY - JOUR

T1 - The effect of quantization on the full configuration interaction quantum Monte Carlo sign problem

AU - Kolodrubetz, M. H.

AU - Spencer, J. S.

AU - Clark, B. K.

AU - Foulkes, W. M C

PY - 2013/1/14

Y1 - 2013/1/14

N2 - The sign problem in full configuration interaction quantum Monte Carlo (FCIQMC) without annihilation can be understood as an instability of the psi-particle population to the ground state of the matrix obtained by making all off-diagonal elements of the Hamiltonian negative. Such a matrix, and hence the sign problem, is basis dependent. In this paper, we discuss the properties of a physically important basis choice: first versus second quantization. For a given choice of single-particle orbitals, we identify the conditions under which the fermion sign problem in the second quantized basis of antisymmetric Slater determinants is identical to the sign problem in the first quantized basis of unsymmetrized Hartree products. We also show that, when the two differ, the fermion sign problem is always less severe in the second quantized basis. This supports the idea that FCIQMC, even in the absence of annihilation, improves the sign problem relative to first quantized methods. Finally, we point out some theoretically interesting classes of Hamiltonians where first and second quantized sign problems differ, and others where they do not.

AB - The sign problem in full configuration interaction quantum Monte Carlo (FCIQMC) without annihilation can be understood as an instability of the psi-particle population to the ground state of the matrix obtained by making all off-diagonal elements of the Hamiltonian negative. Such a matrix, and hence the sign problem, is basis dependent. In this paper, we discuss the properties of a physically important basis choice: first versus second quantization. For a given choice of single-particle orbitals, we identify the conditions under which the fermion sign problem in the second quantized basis of antisymmetric Slater determinants is identical to the sign problem in the first quantized basis of unsymmetrized Hartree products. We also show that, when the two differ, the fermion sign problem is always less severe in the second quantized basis. This supports the idea that FCIQMC, even in the absence of annihilation, improves the sign problem relative to first quantized methods. Finally, we point out some theoretically interesting classes of Hamiltonians where first and second quantized sign problems differ, and others where they do not.

UR - http://www.scopus.com/inward/record.url?scp=84872721326&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872721326&partnerID=8YFLogxK

U2 - 10.1063/1.4773819

DO - 10.1063/1.4773819

M3 - Article

C2 - 23320671

AN - SCOPUS:84872721326

VL - 138

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 2

M1 - 024110

ER -