The Origin of Degeneracies and Crossings in the 1d Hubbard Model

Abstract

The paper is devoted to the connection between integrability of a finite quantum system and degeneracies of its energy levels. In particular, we analyze 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 wave functions of many of these states do not depend on the coupling, which suggests the existence of an additional parameter independent symmetry.

25 pages, 12 figures

Cited by in corpus (27)

• Remarks on the notion of quantum integrability
• Quantum phase transitions in the interacting boson model
• Quantum Chaos in the Bose-Hubbard model
• Quantum Phase Transitions in the Interacting Boson Model: Integrability, level repulsion and level crossing
• Strong Coupling Expansion for the Pairing Hamiltonian
• Quantum integrability in systems with finite number of levels
• The Link between Integrability, Level Crossings, and Exact Solution in Quantum Models
• Quantum integrability in the multistate Landau-Zener problem
• An Exactly Solvable Model for the Integrability-Chaos Transition in Rough Quantum Billiards
• Integrable matrix theory: Level statistics
• Spin hydrodynamics in the S = 1/2 anisotropic Heisenberg chain
• Classification of Parameter-Dependent Quantum Integrable Models, Their Parameterization, Exact Solution, and Other Properties
• A Class of Parameter Dependent Commuting Matrices
• Parameter Dependent Commuting Matrices, Plücker relations and Related Quantum Glass Models
• Strong coupling anomalous dimensions of $\mathcal{N}=4$ super Yang-Mills
• Pairwise quantum correlations in four-level quantum dot systems
• Non-equilibration, synchronization, and time crystals in isotropic Heisenberg models
• Rotationally invariant ensembles of integrable matrices
• Renormalisation and fixed points in Hilbert Space
• Level Crossing in Random Matrices: I. Random perturbation of a fixed matrix
• Intriguing electron correlation effects in the photoionization of metallic quantum--dot nanorings
• Analysis of the N=4 Hubbard ring using a counting operator
• Counting operator analysis of the discrete spectrum of some model Hamiltonians
• Small quenches and thermalization
• Bethe-ansatz studies of energy level crossings in the one-dimensional Hubbard model
• Many-body multi-valuedness of particle-current variance in closed and open cold-atom systems
• AdS/CFT duality at strong coupling