Yuzbashyan, Emil A and Altshuler, Boris L and Shastry, Sriram B (2002) The origin of degeneracies and crossings in the 1d Hubbard model. In: Journal of Physics A: Mathematical and General, 35 (34). pp. 7525-7547.
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The paper is devoted to the connection between integrability of a finite quantum system and degeneracies of its energy levels. In particular, we analyse in detail the energy spectra of finite Hubbard chains. Heilmann and Lieb demonstrated that in these systems there are crossings of levels of the same parameter-independent symmetry. We show that this apparent violation of the Wigner-von Neumann noncrossing rule follows directly from the existence of nontrivial conservation laws and is a characteristic signature of quantum integrability. The energy spectra of Hubbard chains display many instances of permanent (at all values of the coupling) twofold degeneracies that cannot be explained by parameter-independent symmetries. We relate these degeneracies to the different transformation properties of the conserved currents under spatial reflections and the particle-hole transformation and estimate the fraction of doubly degenerate states. We also discuss multiply degenerate eigenstates of the Hubbard Hamiltonian. The wavefunctions of many of these states do not depend on the coupling, which suggests the existence of an additional parameter-independent symmetry.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Institute of Physics.|
|Date Deposited:||27 Jul 2011 06:53|
|Last Modified:||27 Jul 2011 06:53|
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