  A nonperturbative quantum impurity solver is proposed based on a formally
exact hierarchical equations of motion (HEOM) formalism for open quantum
systems. It leads to quantitatively accurate evaluation of physical properties
of strongly correlated electronic systems, in the framework of dynamical
mean-field theory (DMFT). The HEOM method is also numerically convenient to
achieve the same level of accuracy as that using the state-of-the-art numerical
renormalization group impurity solver at finite temperatures. The practicality
of the novel HEOM+DMFT method is demonstrated by its applications to the
Hubbard models with Bethe and hypercubic lattice structures. We investigate the
metal-insulator transition phenomena, and address the effects of temperature on
the properties of strongly correlated lattice systems.
