A Blocked Linear Method for Optimizing Large Parameter Sets in Variational Monte Carlo

We
present a modification to variational Monte Carlo’s linear
method optimization scheme that addresses a critical memory bottleneck
while maintaining compatibility with both the traditional ground state
variational principle and our recently introduced variational principle
for excited states. For wave function ansatzes with tens of thousands
of variables, our modification reduces the required memory per parallel
process from tens of gigabytes to hundreds of megabytes, making the
methodology a much better fit for modern supercomputer architectures
in which data communication and per-process memory consumption are
primary concerns. We verify the efficacy of the new optimization scheme
in small molecule tests involving both the Hilbert space Jastrow antisymmetric
geminal power ansatz and real space multi-Slater Jastrow expansions.
Satisfied with its performance, we have added the optimizer to the
QMCPACK software package, with which we test a systematically convergent,
nonperturbative approach to excitation energies on the example of
a Mott-insulating hydrogen ring.