Representations of commutative electron operator algebras on MPS states for fractional quantum Hall systems

We study the action of several recently discussed second-quantized operator algebras satisfying Newton-Girard relations on matrix product state (MPS) trial wave functions for fractional quantum Hall systems. It is observed that this action generally preserves the MPS structure in a simple and well-defined manner, leading to insertion of bosonic modes into the MPS correlators. Various consequences of this direct translation between physical microscopic and virtual MPS degrees of freedom are discussed. On the one hand, it is intimately tied to the existence of frustration free parent Hamiltonians, notably in the Laughlin and Moore-Read case, but also in mixed-Landau-level situations such as unprojected Jain states. On the other hand, recent proposals for localized quasi-particle states by Bochniak et al. have straightforward MPS representations. Natural, spatially extended bases for such quasi-particle states are discussed.