Twist Boundary Conditions of Quantum Spin Chains near the Gaussian Fixed Points

TL;DR

This paper introduces a novel numerical method using boundary conditions and duality transformations to accurately determine critical points in quantum spin chains near Gaussian fixed points, exemplified on models like Ashkin-Teller.

Contribution

It presents the first explicit application of duality combined with boundary condition manipulation for numerical determination of critical points in quantum spin models.

Findings

Successfully identified critical points using boundary conditions and duality.

Demonstrated the method on Ashkin-Teller and Gaussian models.

Validated the approach with numerical results.

Abstract

Duality transformation, which relates a high-temperature phase to a low-temperature one, is used exactly to determine the critical point for several models (2D Ising, Potts, Ashkin-Teller, 8-vertex), as the self dual condition. By changing boundary condition, numerically we can determine the self-dual(critical) point of the Ashkin-Teller(or Gaussian) model. This is the first explicit application of the duality to the numerical calculation, with the use of boundary conditions.