  We consider the two-dimensional nonlinear Schr\"{o}dinger equation with a
white noise potential, described by the Anderson hamiltonian. After define the
corresponding energy space via the paracontrolled distribution framework from
singular stochastic partial differential equations, we prove the existence of
the minimizer as the least energy solution by studying a minimization problem
of the corresponding energy functional subject to $L^2$ constraints.
Subsequently, we study the regularity of the minimizer, which is a weak
solution of the nonlinear Schr\"{o}dinger equation. Finally, we derive a tail
estimate for the distribution of the principal eigenvalue corresponding to the
least energy solution by energy estimates.
