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

Abstract

A length-N spin chain with the \sqrt{N}(=v)-th 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\ge2 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\le32 spins. As a demonstration, the correlation-length critical exponent $\nu$ is analyzed in some detail.

References in corpus (4)

• Real-space renormalization group for the transverse-field Ising model in two and three dimensions
• Deconfined criticality for the S=1 spin model on the spatially anisotropic triangular lattice
• Eliminated corrections to scaling around a renormalization-group fixed point: Transfer-matrix simulation of an extended d=3 Ising model
• Multicriticality of the (2+1)-dimensional gonihedric model: A realization of the (d,m)=(3,2) Lifshitz point

Cited by in corpus (1)

• Criticalities of the transverse- and longitudinal-field fidelity susceptibilities for the d=2 quantum Ising model