50,339 research outputs found

    Spin-S Kagome quantum antiferromagnets in a field with tensor networks

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    Spin-SS Heisenberg quantum antiferromagnets on the Kagome lattice offer, when placed in a magnetic field, a fantastic playground to observe exotic phases of matter with (magnetic analogs of) superfluid, charge, bond or nematic orders, or a coexistence of several of the latter. In this context, we have obtained the (zero temperature) phase diagrams up to S=2S=2 directly in the thermodynamic limit thanks to infinite Projected Entangled Pair States (iPEPS), a tensor network numerical tool. We find incompressible phases characterized by a magnetization plateau vs field and stabilized by spontaneous breaking of point group or lattice translation symmetry(ies). The nature of such phases may be semi-classical, as the plateaus at 13\frac{1}{3}th, (1−29S)(1-\frac{2}{9S})th and (1−19S)(1-\frac{1}{9S})th of the saturated magnetization (the latter followed by a macroscopic magnetization jump), or fully quantum as the spin-12\frac{1}{2} 19\frac{1}{9}-plateau exhibiting coexistence of charge and bond orders. Upon restoration of the spin rotation U(1)U(1) symmetry a finite compressibility appears, although lattice symmetry breaking persists. For integer spin values we also identify spin gapped phases at low enough field, such as the S=2S=2 (topologically trivial) spin liquid with no symmetry breaking, neither spin nor lattice.Comment: 5 pages, 3 figures, 1 table + supplemental materia

    A scattering of orders

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    A linear ordering is scattered if it does not contain a copy of the rationals. Hausdorff characterised the class of scattered linear orderings as the least family of linear orderings that includes the class B \mathcal B of well-orderings and reversed well-orderings, and is closed under lexicographic sums with index set in B \mathcal B. More generally, we say that a partial ordering is Îș \kappa -scattered if it does not contain a copy of any Îș \kappa -dense linear ordering. We prove analogues of Hausdorff's result for Îș \kappa -scattered linear orderings, and for Îș \kappa -scattered partial orderings satisfying the finite antichain condition. We also study the QÎș \mathbb{Q}_\kappa -scattered partial orderings, where QÎș \mathbb{Q}_\kappa is the saturated linear ordering of cardinality Îș \kappa , and a partial ordering is QÎș \mathbb{Q}_\kappa -scattered when it embeds no copy of QÎș \mathbb{Q}_\kappa . We classify the QÎș \mathbb{Q}_\kappa -scattered partial orderings with the finite antichain condition relative to the QÎș \mathbb{Q}_\kappa -scattered linear orderings. We show that in general the property of being a QÎș \mathbb{Q}_\kappa -scattered linear ordering is not absolute, and argue that this makes a classification theorem for such orderings hard to achieve without extra set-theoretic assumptions

    On structures in hypergraphs of models of a theory

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    We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types of models of a theory, are given
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