  We develop a time-dependent variational Monte Carlo (t-VMC) method for
quantum dynamics of strongly correlated electrons. The t-VMC method has been
recently applied to bosonic systems and quantum spin systems. Here, we propose
a time-dependent trial wave function with many variational parameters, which is
suitable for nonequilibrium strongly correlated electron systems. As the trial
state, we adopt the generalized pair-product wave function with correlation
factors and quantum-number projections. This trial wave function has been
proven to accurately describe ground states of strongly correlated electron
systems. To show the accuracy and efficiency of our trial wave function in
nonequilibrium states as well, we present our benchmark results for relaxation
dynamics during and after interaction quench protocols of fermionic Hubbard
models. We find that our trial wave function well reproduces the exact results
for the time evolution of physical quantities such as energy, momentum
distribution, spin structure factor, and superconducting correlations. These
results show that the t-VMC with our trial wave function offers an efficient
and accurate way to study challenging problems of nonequilibrium dynamics in
strongly correlated electron systems.
