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The paper is devoted to the connection between integrability of a finitequantum system and degeneracies of its energy levels. In particular, we analyzein detail the energy spectra of finite Hubbard chains. Heilmann and Liebdemonstrated that in these systems there are crossings of levels of the sameparameter independent symmetry. We show that this apparent violation of theWigner-von Neumann noncrossing rule follows directly from the existence ofnontrivial conservation laws and is a characteristic signature of quantumintegrability. The energy spectra of Hubbard chains display many instances ofpermanent (at all values of the coupling) twofold degeneracies that cannot beexplained by parameter independent symmetries. We relate these degeneracies tothe different transformation properties of the conserved currents under spatialreflections and the particle-hole transformation and estimate the fraction ofdoubly degenerate states. We also discuss multiply degenerate eigenstates ofthe Hubbard Hamiltonian. The wave functions of many of these states do notdepend on the coupling, which suggests the existence of an additional parameterindependent symmetry.Comment: 25 pages, 12 figure

The origin of degeneracies and crossings in the 1d Hubbard model