### Abstract

A length-N spin chain with the √N(=v) neighbor interaction is identical to a two-dimensional (d = 2) model under the screw-boundary (SB) condition. The SB condition provides a flexible scheme to construct a d ≥ 2 cluster from an arbitrary number of spins; the numerical diagonalization combined with the SB condition admits a potential applicability to a class of systems intractable with the quantum Monte Carlo method due to the negative-sign problem. However, the simulation results suffer from characteristic finite-size corrections inherent in SB. In order to suppress these corrections, we adjust the screw pitch v(N) so as to minimize the excitation gap for each N. This idea is adapted to the transverse-field Ising model on the triangular lattice with N ≤ 32 spins. As a demonstration, the correlation-length critical exponent ν is analyzed in some detail.

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

Article number | P08020 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2011 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 2011 |

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### Keywords

- finite-size scaling
- other numerical approaches

### ASJC Scopus subject areas

- Statistics and Probability
- Statistical and Nonlinear Physics
- Statistics, Probability and Uncertainty

### Cite this

**D = 2 transverse-field Ising model under the screw-boundary condition : An optimization of the screw pitch.** / Nishiyama, Yoshihiro.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - D = 2 transverse-field Ising model under the screw-boundary condition

T2 - An optimization of the screw pitch

AU - Nishiyama, Yoshihiro

PY - 2011/8

Y1 - 2011/8

N2 - A length-N spin chain with the √N(=v) neighbor interaction is identical to a two-dimensional (d = 2) model under the screw-boundary (SB) condition. The SB condition provides a flexible scheme to construct a d ≥ 2 cluster from an arbitrary number of spins; the numerical diagonalization combined with the SB condition admits a potential applicability to a class of systems intractable with the quantum Monte Carlo method due to the negative-sign problem. However, the simulation results suffer from characteristic finite-size corrections inherent in SB. In order to suppress these corrections, we adjust the screw pitch v(N) so as to minimize the excitation gap for each N. This idea is adapted to the transverse-field Ising model on the triangular lattice with N ≤ 32 spins. As a demonstration, the correlation-length critical exponent ν is analyzed in some detail.

AB - A length-N spin chain with the √N(=v) neighbor interaction is identical to a two-dimensional (d = 2) model under the screw-boundary (SB) condition. The SB condition provides a flexible scheme to construct a d ≥ 2 cluster from an arbitrary number of spins; the numerical diagonalization combined with the SB condition admits a potential applicability to a class of systems intractable with the quantum Monte Carlo method due to the negative-sign problem. However, the simulation results suffer from characteristic finite-size corrections inherent in SB. In order to suppress these corrections, we adjust the screw pitch v(N) so as to minimize the excitation gap for each N. This idea is adapted to the transverse-field Ising model on the triangular lattice with N ≤ 32 spins. As a demonstration, the correlation-length critical exponent ν is analyzed in some detail.

KW - finite-size scaling

KW - other numerical approaches

UR - http://www.scopus.com/inward/record.url?scp=80053544984&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053544984&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2011/08/P08020

DO - 10.1088/1742-5468/2011/08/P08020

M3 - Article

VL - 2011

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 8

M1 - P08020

ER -