2,056 research outputs found
Phase diagram of an extended quantum dimer model on the hexagonal lattice
We introduce a quantum dimer model on the hexagonal lattice that, in addition
to the standard three-dimer kinetic and potential terms, includes a competing
potential part counting dimer-free hexagons. The zero-temperature phase diagram
is studied by means of quantum Monte Carlo simulations, supplemented by
variational arguments. It reveals some new crystalline phases and a cascade of
transitions with rapidly changing flux (tilt in the height language). We
analyze perturbatively the vicinity of the Rokhsar-Kivelson point, showing that
this model has the microscopic ingredients needed for the "devil's staircase"
scenario [E. Fradkin et al., Phys. Rev. B 69, 224415 (2004)], and is therefore
expected to produce fractal variations of the ground-state flux.Comment: Published version. 5 pages + 8 (Supplemental Material), 31
references, 10 color figure
Entanglement scaling in critical two-dimensional fermionic and bosonic systems
We relate the reduced density matrices of quadratic bosonic and fermionic
models to their Green's function matrices in a unified way and calculate the
scaling of bipartite entanglement of finite systems in an infinite universe
exactly. For critical fermionic 2D systems at T=0, two regimes of scaling are
identified: generically, we find a logarithmic correction to the area law with
a prefactor dependence on the chemical potential that confirms earlier
predictions based on the Widom conjecture. If, however, the Fermi surface of
the critical system is zero-dimensional, we find an area law with a
sublogarithmic correction. For a critical bosonic 2D array of coupled
oscillators at T=0, our results show that entanglement follows the area law
without corrections.Comment: 4 pages, 4 figure
Transfer ideals and torsion in the Morava -theory of abelian groups
Let be a finite abelian group of rank at least . We show that , the quotient of the Morava -cohomology of by the ideal generated by the image of the transfers along all proper subgroups, contains -torsion. The proof makes use of transchromatic character theory
Chromatic fracture cubes
In this note, we construct a general form of the chromatic fracture cube, using a convenient characterization of the total homotopy fiber, and deduce a decomposition of the E(n)-local stable homotopy category
Magnetism, coherent many-particle dynamics, and relaxation with ultracold bosons in optical superlattices
We study how well magnetic models can be implemented with ultracold bosonic
atoms of two different hyperfine states in an optical superlattice. The system
is captured by a two-species Bose-Hubbard model, but realizes in a certain
parameter regime actually the physics of a spin-1/2 Heisenberg magnet,
describing the second order hopping processes. Tuning of the superlattice
allows for controlling the effect of fast first order processes versus the
slower second order ones.
Using the density-matrix renormalization-group method, we provide the
evolution of typical experimentally available observables. The validity of the
description via the Heisenberg model, depending on the parameters of the
Hubbard model, is studied numerically and analytically. The analysis is also
motivated by recent experiments [S. Foelling et al., Nature 448, 1029 (2007);
S. Trotzky et al., Sience 319, 295 (2008)] where coherent two-particle dynamics
with ultracold bosonic atoms in isolated double wells were realized. We provide
theoretical background for the next step, the observation of coherent
many-particle dynamics after coupling the double wells. Contrary to the case of
isolated double wells, relaxation of local observables can be observed. The
tunability between the Bose-Hubbard model and the Heisenberg model in this
setup could be used to study experimentally the differences in equilibration
processes for nonintegrable and Bethe ansatz integrable models. We show that
the relaxation in the Heisenberg model is connected to a phase averaging
effect, which is in contrast to the typical scattering driven thermalization in
nonintegrable models. We discuss the preparation of magnetic groundstates by
adiabatic tuning of the superlattice parameters.Comment: 20 pages, 24 figures; minor changes, published versio
On conjectures of Hovey-Strickland and Chai
We prove the height two case of a conjecture of Hovey and Strickland that provides a -local analogue of the Hopkins--Smith thick subcategory theorem. Our approach first reduces the general conjecture to a problem in arithmetic geometry posed by Chai. We then use the Gross--Hopkins period map to verify Chai's Hope at height two and all primes. Along the way, we show that the graded commutative ring of completed cooperations for Morava -theory is coherent, and that every finitely generated Morava module can be realized by a -local spectrum as long as . Finally, we deduce consequences of our results for descent of Balmer spectra
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