  Mean-field theory (MFT) is one of the main available tools for analytical
calculations entailed in investigations regarding many-body systems. Recently,
there have been an urge of interest in ameliorating this kind of method, mainly
with the aim of incorporating geometric and correlation properties of these
systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded
quite well in doing that for classical spin systems. Nevertheless, even the
CCMFT presents some deficiencies when applied to quantum systems. In this
article, we address this issue by proposing the quantum CCMFT (QCCMFT), which,
in contrast to its former approach, uses general quantum states in its
self-consistent mean-field equations. We apply the introduced QCCMFT to the
transverse Ising model in honeycomb, square, and simple cubic lattices and
obtain fairly good results both for the Curie temperature of thermal phase
transition and for the critical field of quantum phase transition. Actually,
our results match those obtained via exact solutions, series expansions or
Monte Carlo simulations.
