Bruno Nachtergaele

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A number of interesting features of the ground states of quantum spin chains are analyzed with the help of a functional integral representation of the system's equilibrium states. Methods of general applicability are introduced in the context of the SU(2S+l)-invariant quantum spin-S chains with the interaction — P, where P is the projection onto the singlet(More)
Complex networks possess a rich, multiscale structure reflecting the dynamical and functional organization of the systems they model. Often there is a need to analyze multiple networks simultaneously, to model a system by more than one type of interaction, or to go beyond simple pairwise interactions, but currently there is a lack of theoretical and(More)
(1.1) i∂tψ(t) = Hψ(t) . For all initial conditions ψ(0) ∈ H, the unique solution is given by ψ(t) = e−itHψ(0), for all t ∈ R. Due to Stone’s Theorem e−itH is a strongly continuous one-parameter group of unitary operators on H, and the self-adjointness of H is the necessary and sufficient condition for the existence of a unique continuous solution for all(More)
We show that the ground states of the three-dimensional XXZ Heisenberg ferromagnet with a 111 interface have excitations localized in a subvolume of linear size R with energies bounded by O(1/R). As part of the proof we show the equivalence of ensembles for the 111 interface states in the following sense: In the thermodynamic limit the states with fixed(More)
Abstract. For a large class of finite-range quantum spin models with half-integer spins, we prove that uniqueness of the ground state implies the existence of a low-lying excited state. For systems of linear size L, with arbitrary finite dimension, we obtain an upper bound on the excitation energy (i.e., the gap above the ground state) of the form (C(More)