Boundary conformal spectrum and surface critical behaviors of the classical spin systems: a tensor network renormalization study

TL;DR

This study uses tensor network renormalization to numerically analyze the boundary conformal spectrum of classical spin models on a 2D lattice, confirming BCFT predictions for surface critical behaviors.

Contribution

It extends tensor network renormalization to open boundary conditions, enabling accurate extraction of boundary conformal spectra for classical spin models.

Findings

Conformal spectra match BCFT predictions for Ising, tri-critical Ising, and 3-state Potts models.

Validates the use of tensor networks for boundary critical phenomena.

Confirms surface critical behaviors align with theoretical BCFT analyses.

Abstract

We numerically obtain the conformal spectrum of several classical spin models on a two-dimensional lattice with open boundaries, for every boundary fixed point obtained by the Cardy's derivation [J. L. Cardy, Nucl. Phys. B 324, 581 (1989)]. In order to extract accurate conformal data, we implement the tensor network renormalization algorithm [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] extended so as to be applicable to a square lattice with open boundaries. We successfully compute the boundary conformal spectrum consistent with the underlying boundary conformal field theories (BCFTs) for the Ising, tri-critical Ising, and 3-state Potts models on the lattice, which allows us to confirm the validity of the BCFT analyses for the surface critical behaviors of those lattice models.