1212.3833 (David Jennings et al.)

Variational quantum field states with symmetry: The continuum limit of a
projected entangled pair state    [PDF]

David Jennings, Jutho Haegeman, Tobias J. Osborne, Frank Verstraete

We obtain a well-behaved continuum limit of projected entangled pair states (PEPS) that provides an abstract class of quantum field states with natural symmetries. Making use of the recently introduced path integral representation of one-dimensional continuous matrix product states (cMPS) for quantum fields, we demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of euclidean symmetries on the physical system requires that the auxiliary system involved in the class' definition must be Lorentz invariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of the lower dimensional auxiliary field system.

View original: http://arxiv.org/abs/1212.3833