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 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 work 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 hx 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 hx=2.5 and
0.5% for the more challenging case of hx=2.9 close to the quantum
critical point at hx=3.04438(2).Comment: published version, presentation improve