We perform imaginary time evolution of an infinite projected entangled pair state (iPEPS) to simulate strongly correlated systems at finite temperature. First, we simulate the Shastry-Sutherland in a magnetic field [1]. We focus on the phase transition into the m=1/2 magnetization plateau, which was observed in experiments on SrCu_2(BO_3)_2. We use the full update algorithm combined with the simple update applied during the initial part of the evolution. We provide an accurate estimate of the critical temperature and estimate critical exponents of the transition. Second, we apply the neighbourhood tensor update algorithm [2] to simulate thermodynamic properties of the Hubbard model [3]. With U(1)xU(1) symmetry and the bond dimensions up to 29, we generate thermal states down to the temperature of 0.17 times the hopping rate. We obtain results for spin and charge correlators measurable in prospective ultra cold atom experiments.
[1] P. Czarnik, M. M. Rams. P. Corboz. J. Dziarmaga, Phys. Rev. B, 103, 075113 (2021)
[2] J. Dziarmaga, Phys. Rev. B, 104, 094411 (2021)
[3] A. Sinha, M. M. Rams, P. Czarnik, J. Dziarmaga, arXiv:2208:xxxx