LAUSR

An infinite projected entangled pair state (iPEPS) is a tensor network ansatz to represent a quantum state on an infinite 2D lattice whose accuracy is controlled by the bond dimension $D$. Its real, Lindbladian, or imaginary time evolution can be split into small time steps. Every time step generates a new iPEPS with an enlarged bond dimension ${D}^{\ensuremath{'}}gD$, which is approximated by an iPEPS with the original $D$. In P. Czarnik and J. Dziarmaga, Phys. Rev. B 98, 045110 (2018), an algorithm was introduced to optimize the approximate iPEPS by maximizing directly its fidelity to the one with the enlarged bond dimension ${D}^{\ensuremath{'}}$. In this paper, we implement a more efficient optimization employing a local estimator of the fidelity. For imaginary time evolution of a thermal state's purification, we also consider using unitary disentangling gates acting on ancillas to reduce the required $D$. We test the algorithm simulating Lindbladian evolution and unitary evolution after a sudden quench of transverse field ${h}_{x}$ in the 2D quantum Ising model. Furthermore, we simulate thermal states of this model and estimate the critical temperature with good accuracy: $0.1%$ for ${h}_{x}=2.5$ and $0.5%$ for the more challenging case of ${h}_{x}=2.9$ close to the quantum critical point at ${h}_{x}=3.04438(2)$.