  Two of the primary sources of error in the Cluster dynamical mean-field
theory (CDMFT) technique arise from the use of finite size clusters and finite
size baths, which makes the development of impurity solvers that can treat
larger systems an essential goal. In this work we introduce an impurity solver
based on the recently developed dynamical variational Monte Carlo (dVMC)
method. Variational Monte Carlo possesses a favorable scaling as a function of
system size, which enables the treatment of systems beyond the reach of current
exact diagonalization solvers. To benchmark the technique, we perform a
systematic set of CDMFT calculations on the one-dimensional Hubbard model. We
compare to results obtained with an exact diagonalization solver for small
clusters, and against the exact solution in the thermodynamic limit obtained by
Lieb and Wu for larger clusters. The development of improved impurity solvers
will help extend the reach of quantum cluster methods, which can be applied to
a wide range of strongly-correlated electron systems, promising new insights on
their emergent behavior.
