In this talk I will explain recent progress on numerical algorithms that use tensor network representations of quantum states to simulate 2-dimensional quantum lattice systems of infinite size. In particular, I will focus on methods which use an infinite Tensor Product State (TPS) - or Projected Entangled Pair State (PEPS) - as the underlying tensor network. I will discuss how these methods can be adapted to numerically compute the physical properties of the system at hand in a variety of ways, and explain current results and research directions.
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