A new method to calculate a 2d ising universality transition point : application near the ashkin-teller multicritical point

TL;DR

This paper introduces a novel numerical method using twisted boundary conditions to accurately determine transition points in 2D Ising universality class models, especially near multicritical points with diverging correlation lengths.

Contribution

The paper presents a new approach employing twisted boundary conditions to suppress finite size effects, enabling precise calculation of transition points near multicritical points in quantum spin models.

Findings

Improved convergence of transition point calculations near multicritical points.

Successful application to the S=1/2 bond-alternating XXZ model.

Accurate determination of the BKT transition point.

Abstract

We propose a new method to numerically calculate transition points that belongs to 2D Ising universality class for quantum spin models. Generally, near the multicritical point, in conventional methods, a finite size correction becomes very large. To suppress the effect of the multicritical point, we use a z-axis twisted boundary condition and a y-axis twisted boundary condition. We apply our method to an S = 1/2 bond-alternating XXZ model. The multicritical point of this model has a BKT transition, where the correlation length diverges singularly. However, with our method, the convergence of calculation is highly improved, thus we can calculate the transition point even near the multicritical point.