### Abstract

We present a numerically stable Quantum Monte Carlo algorithm to calculate zero-temperature imaginary-time Green functions G(r, τ) for Hubbard type models. We illustrate the efficiency of the algorithm by calculating the on-site Green function G(r = 0, τ) on 4 × 4 to 12 × 12 lattices for the two-dimensional half-filled repulsive Hubbard model at U/t = 4. By fitting the tail of G(r = 0, τ) at long imaginary time to the form e^{-τΔε}, we obtain a precise estimate of the charge gap: Δ_{c} = 0.67±0.02 in units of the hopping matrix element. We argue that the algorithm provides a powerful tool to study the metal-insulator transition from the insulator side.

Original language | English |
---|---|

Pages (from-to) | 189-194 |

Number of pages | 6 |

Journal | Journal of the Physical Society of Japan |

Volume | 65 |

Issue number | 1 |

Publication status | Published - 1996 Dec 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Hubbard gap
- Hubbard model
- Quantum Monte Carlo
- Zero-temperature Green functions

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*65*(1), 189-194.

**Stable Quantum Monte Carlo Algorithm for T= 0 Calculation of Imaginary Time Green Functions.** / Assaad, Fakher F.; Imada, Masatoshi.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 65, no. 1, pp. 189-194.

}

TY - JOUR

T1 - Stable Quantum Monte Carlo Algorithm for T= 0 Calculation of Imaginary Time Green Functions

AU - Assaad, Fakher F.

AU - Imada, Masatoshi

PY - 1996/12/1

Y1 - 1996/12/1

N2 - We present a numerically stable Quantum Monte Carlo algorithm to calculate zero-temperature imaginary-time Green functions G(r, τ) for Hubbard type models. We illustrate the efficiency of the algorithm by calculating the on-site Green function G(r = 0, τ) on 4 × 4 to 12 × 12 lattices for the two-dimensional half-filled repulsive Hubbard model at U/t = 4. By fitting the tail of G(r = 0, τ) at long imaginary time to the form e-τΔε, we obtain a precise estimate of the charge gap: Δc = 0.67±0.02 in units of the hopping matrix element. We argue that the algorithm provides a powerful tool to study the metal-insulator transition from the insulator side.

AB - We present a numerically stable Quantum Monte Carlo algorithm to calculate zero-temperature imaginary-time Green functions G(r, τ) for Hubbard type models. We illustrate the efficiency of the algorithm by calculating the on-site Green function G(r = 0, τ) on 4 × 4 to 12 × 12 lattices for the two-dimensional half-filled repulsive Hubbard model at U/t = 4. By fitting the tail of G(r = 0, τ) at long imaginary time to the form e-τΔε, we obtain a precise estimate of the charge gap: Δc = 0.67±0.02 in units of the hopping matrix element. We argue that the algorithm provides a powerful tool to study the metal-insulator transition from the insulator side.

KW - Hubbard gap

KW - Hubbard model

KW - Quantum Monte Carlo

KW - Zero-temperature Green functions

UR - http://www.scopus.com/inward/record.url?scp=0030530187&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030530187&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030530187

VL - 65

SP - 189

EP - 194

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 1

ER -