50,339 research outputs found
Spin-S Kagome quantum antiferromagnets in a field with tensor networks
Spin- 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 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 th, th and
th of the saturated magnetization (the latter followed by a
macroscopic magnetization jump), or fully quantum as the spin-
-plateau exhibiting coexistence of charge and bond orders. Upon
restoration of the spin rotation 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
(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
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 of well-orderings and reversed well-orderings, and is closed under lexicographic sums with index set in . More generally, we say that a partial ordering is -scattered if it does not contain a copy of any -dense linear ordering. We prove analogues of Hausdorff's result for -scattered linear orderings, and for -scattered partial orderings satisfying the finite antichain condition. We also study the -scattered partial orderings, where is the saturated linear ordering of cardinality , and a partial ordering is -scattered when it embeds no copy of . We classify the -scattered partial orderings with the finite antichain condition relative to the -scattered linear orderings. We show that in general the property of being a -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
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
- âŠ