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

An optimization of the screw pitch

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Article numberP08020
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2011
Issue number8
DOIs
Publication statusPublished - Aug 2011

Fingerprint

screws
Ising model
Ising Model
Transverse
boundary conditions
Boundary conditions
optimization
Optimization
Quantum Monte Carlo
Spin Chains
Triangular Lattice
Diagonalization
Correlation Length
Monte Carlo method
Critical Exponents
Excitation
Minimise
Arbitrary
Interaction
exponents

Keywords

  • finite-size scaling
  • other numerical approaches

ASJC Scopus subject areas

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

Cite this

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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.",
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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.

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