Towards neural network quantum states with nonabelian symmetries

Although artificial neural networks have recently been proven to provide a promising new framework for constructing quantum many-body wave functions, the parameterization of a quantum wavefunction with nonabelian symmetries in terms of a Boltzmann machine inherently leads to biased results due to the basis dependence. We demonstrate that this problem can be overcome by sampling in the basis of irreducible representations instead of spins, for which the corresponding ansatz respects the nonabelian symmetries of the system. We will show that this representation is connected to symmetric tensor network states.

We apply our methodology to find the ground states of the one-dimensional antiferromagnetic Heisenberg (AFH) model with spin-half and spin-1 degrees of freedom. The proposed ansatz can target excited states, which is illustrated by calculating the energy gap of the AFH model.

Implementing non-abelian symmetries in variational quantum states is an important step towards solving frustrated quantum systems. We demonstrate recent results using our ansatz on the frustrated J1-J2 model.