Continuous Tensor Network States for Quantum Fields

  title={Continuous Tensor Network States for Quantum Fields},
  author={Antoine Tilloy and Juan Ignacio Cirac},
  journal={Physical Review X},
We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean invariant, and are genuine continuum limits of discrete tensor network states. Admitting both a functional integral and an operator representation, they share the important properties of their discrete counterparts: expressiveness, invariance under gauge… 

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