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

TL;DR

This paper optimizes the screw pitch in a d=2 transverse-field Ising model with screw-boundary conditions to reduce finite-size corrections, enabling more accurate numerical analysis of critical properties.

Contribution

It introduces a method to adjust the screw pitch v(N) to minimize finite-size effects in the screw-boundary condition for quantum spin models.

Findings

Optimized screw pitch reduces finite-size corrections.

Accurate estimation of the correlation-length critical exponent ν.

Demonstration on a triangular lattice with up to 32 spins.

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.