Characterizing symmetries in a projected entangled pair state

TY - JOUR

T1 - Characterizing symmetries in a projected entangled pair state

AU - Perez-Garcia, D.

AU - Sanz, M.

AU - Gonzalez-Guillen, C. E.

AU - Wolf, Michael Marc

AU - Cirac, J. I.

PY - 2010/2/26

Y1 - 2010/2/26

N2 - We show that two different tensors defining the same translational invariant injective projected entangled pair state (PEPS) in a square lattice must be the same up to a trivial gauge freedom. This allows us to characterize the existence of any local or spatial symmetry in the state. As an application of these results we prove that a SU(2) invariant PEPS with half-integer spin cannot be injective, which can be seen as a Lieb-Shultz-Mattis theorem in this context. We also give the natural generalization for U(1) symmetry in the spirit of Oshikawa-Yamanaka-Affleck, and show that a PEPS with Wilson loops cannot be injective.

AB - We show that two different tensors defining the same translational invariant injective projected entangled pair state (PEPS) in a square lattice must be the same up to a trivial gauge freedom. This allows us to characterize the existence of any local or spatial symmetry in the state. As an application of these results we prove that a SU(2) invariant PEPS with half-integer spin cannot be injective, which can be seen as a Lieb-Shultz-Mattis theorem in this context. We also give the natural generalization for U(1) symmetry in the spirit of Oshikawa-Yamanaka-Affleck, and show that a PEPS with Wilson loops cannot be injective.

U2 - 10.1088/1367-2630/12/2/025010

DO - 10.1088/1367-2630/12/2/025010

M3 - Journal article

SN - 1367-2630

VL - 12

SP - 025010

JO - New Journal of Physics

JF - New Journal of Physics

ER -