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

Abstract

We study second-order finite-temperature phase transitions of the two-dimensional quantum Ising and interacting honeycomb fermion models using infinite projected entangled pair states (iPEPS). We obtain an iPEPS thermal state representation by variational tensor network renormalization. We find that at the critical temperature Tc 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 Tc and the universal critical exponents. We find that in the vicinity of Tc the behavior of observables follows well the one predicted by FCLS. Using FCLS we obtain Tc and the critical exponents in agreement with quantum Monte Carlo results except for couplings close to the quantum critical points where larger bond dimensions are required.