## Exactly soluble tensor network model in 2+1D with U(1) symmetry and quantize Hall conductance

#### Xiao-Gang WenMassachusetts Institute of Technology

It has been challenging to construct an exactly soluble (or fixed-point) tensor network path integral to realize a phase with non-zero Hall conductance. In this talk, I will describe one such construction, using the group cohomology description of of U(1) SPT phase and the cocycle formalism. The exactly soluble path integral give rise to a commuting projector Hamiltonian whose ground state has a quantize Hall conductance.

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