# Phase boundary location with information-theoretic entropy in tensor renormalization group flows

## TL;DR

This paper introduces a tensor network method that uses information-theoretic entropy to accurately identify phase boundaries in two-dimensional classical lattice models, showing strong agreement with known results.

## Contribution

The paper presents a novel, efficient entropy-based tensor network approach for locating phase transitions, applicable to various types of phase changes in lattice models.

## Key findings

- Accurately locates phase boundaries in Potts models with different transition types.
- Shows good agreement with Monte Carlo results for the J1-J2 Ising model.
- Demonstrates effectiveness across first-order, weakly first-order, and continuous transitions.

## Abstract

We present a simple and efficient tensor network method to accurately locate phase boundaries of two-dimensional classical lattice models. The method utilizes only the information-theoretic (von Neumann) entropy of quantities that automatically arise along tensor renormalization group [Phys. Rev. Lett. \textbf{12}, 120601 (2007)] flows of partition functions. We benchmark the method against theoretically known results for the square-lattice $q$-state Potts models, which includes first-order, weakly first-order, and continuous phase transitions, and find good agreement in all cases. We also compare against previous Monte Carlo results for the frustrated square lattice $J_1-J_2$ Ising model and find good agreement.