Tensor network calculation of boundary and corner magnetization

TL;DR

This paper introduces a modified CTMRG algorithm that measures boundary and corner magnetization in lattice systems, utilizing automatic differentiation to accurately compute critical exponents.

Contribution

The work presents a novel modification of the CTMRG algorithm to measure boundary magnetization and employs automatic differentiation for precise critical exponent calculation.

Findings

Successful measurement of boundary and corner magnetization

Accurate determination of the boundary critical exponent β

Enhanced computational method for boundary critical phenomena

Abstract

The Corner Transfer Matrix Renormalization Group (CTMRG) algorithm is modified to measure the magnetization at the boundary of the system, including the corners of the square-shaped lattice. Using automatic differentiation, we calculate the magnetization's first derivative, allowing us to determine the boundary critical exponent $\beta$ accurately.