# Finite correlation length scaling with infinite projected entangled pair states at finite temperature

## TL;DR

This paper applies finite correlation length scaling to iPEPS thermal states to accurately determine critical temperatures and exponents of 2D quantum phase transitions at finite temperature.

## Contribution

It demonstrates the effectiveness of FCLS in extracting critical properties from iPEPS thermal states at finite temperature, extending previous zero-temperature methods.

## Key findings

- FCLS accurately estimates $T_c$ and critical exponents near phase transitions.
- Correlation length remains finite at $T_c$ for accessible bond dimensions.
- Results agree with Quantum Monte Carlo except near quantum critical points.

## Abstract

We study second order finite temperature phase transitions of the 2D quantum Ising and interacting honeycomb fermions models using infinite projected entangled pair states (iPEPS). We obtain an iPEPS thermal state representation by Variational Tensor Network Renormalization (VTNR). We find that at the critical temperature $T_c$ the iPEPS correlation length is finite for the computationally accessible values of the iPEPS bond dimension $D$. Motivated by this observation we investigate the application of Finite Correlation Length Scaling (FCLS), which has been previously used for iPEPS simulations of quantum critical points at $T=0$, to obtain precise values of $T_c$ and the universal critical exponents. We find that in the vicinity of $T_c$ the behavior of observables follows well the one predicted by FCLS. Using FCLS we obtain $T_c$ and the critical exponents in agreement with Quantum Monte Carlo (QMC) results except for couplings close to the quantum critical points where larger bond dimensions are required.