Under the Morse-Bott condition the Gross-Pitaevskii ground-state set partitions into finitely many symmetry orbits, which is exactly the threshold for local Q-linear convergence of P-RG methods.
Zhang, Exponential convergence of Sobolev gradient descent for a class of nonlinear eigenproblems
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Structure and symmetry of the Gross-Pitaevskii ground-state manifold
Under the Morse-Bott condition the Gross-Pitaevskii ground-state set partitions into finitely many symmetry orbits, which is exactly the threshold for local Q-linear convergence of P-RG methods.