Equivariant Variational Monte Carlo for quantum systems

Variational Monte Carlo algorithms based on sampling basis states in a computational basis often suffer from breaking of SU(2)-symmetry when the basis states transform non-trivially under the symmetry group.  We propose two ways to solve this issue.  On one hand, we construct basis states that transform trivially under the continuous SU(2) symmetry group, and use them as input states of a suitable variational wave function.  On the other hand, we move the transformation requirements of SU(2) to the variational wave function, allowing us to use simple basis states as its input.  In this way, we reconcile SU(2) symmetry with basis states defined on the local degrees of freedom, allowing us to additionally include lattice symmetries.  We show that both constructions lead to accurate variational states on antiferromagnetic and frustrated heisenberg systems in one and two dimensions.