  In this work, we present an analytical theory of strongly correlated Wigner
crystals (WCs) in the lowest Landau level (LLL) by constructing an approximate,
but accurate effective two-body interaction for composite fermions (CFs)
participating in the WCs. This requires integrating out the degrees of freedom
of all surrounding CFs, which we accomplish analytically by approximating their
wave functions by delta functions. This method produces energies of various
strongly correlated WCs that are in excellent agreement with those obtained
from the Monte Carlo simulation of the full CF crystal wave functions. We
compute the compressibility of the strongly correlated WCs in the LLL and
predict discontinuous changes at the phase boundaries separating different
crystal phases.
