Fermionic isometric tensor network states in 2D

In one dimension, the density-matrix renormalization group (DMRG) algorithm gives practically exact ground state wavefunctions and energies for gapped systems and good approximations of ground states for gapless systems. The success of 1D DMRG relies on the structure of tensor network states (TNS), an efficient representation of

quantum states with primarily local entanglement. Unlike in 1D, the exact computation of any physical expectation value of higher-dimensional TNS is exponentially hard. Recently, Michael Zaletel and Frank Pollman proposed a new ansatz isometric TNS (isoTNS), providing a solution to this problem and opening the possibility of a 2D DMRG algorithm. We generalize the definition to fermionic systems, discuss the representability of fermionic isoTNS, and benchmark a real-time/imaginary-time evolution algorithm.