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We propose an efficient algorithm for simulating quantum many-body systems intwo spatial dimensions using projected entangled pair states. This is done byapproximating the environment, arising in the context of updating tensors inthe process of time evolution, using a single-layered tensor network structure.This significantly reduces the computational costs and allows simulations in alarger submanifold of the Hilbert space as bounded by the bond dimension of thetensor network. We present numerical evidence for stability of the method on anantiferromagnetic isotropic Heisenberg model where good agreement is found withthe available accurate results.

Time evolution of projected entangled pair states in the single layer picture