Time evolution of an infinite projected entangled pair state: An efficient algorithm

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' > D, 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'. 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, 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).