D = 2 transverse-field Ising model under the screw-boundary condition: An optimization of the screw pitch

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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.

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

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