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