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Abstract

We study the interplay between symmetry representations of the physical and
virtual space on the class of tensor network states for critical spins systems
known as field tensor network states (fTNS). These are by construction infinite
dimensional tensor networks whose virtual space is described by a conformal
field theory (CFT). We can represent a symmetry on the physical index as a
commutator with the corresponding CFT current on the virtual space. By then
studying this virtual space representation we can learn about the critical
symmetry protected topological properties of the state, akin to the
classification of symmetry protected topological order for matrix product
states. We use this to analytically derive the critical symmetry protected
topological properties of the two ground states of the Majumdar-Ghosh point
with respect to the previously defined symmetries.