Charge Density Bounds in Superconducting States of Strongly Correlated Systems

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Charge density bounds of knotted and linked vortex states in two-component Ginzburg-Landau model are considered. When the mutual linking number of vector order parameter vortex lines is less than the Hopf invariant, these states have the lower-lying energies. It is shown that a set of local minima of free energy contains new classes of universality which exist in a hole density range limited at both finite ends.