1,244 research outputs found
Random Walks on Hypergraphs with Edge-Dependent Vertex Weights
Hypergraphs are used in machine learning to model higher-order relationships
in data. While spectral methods for graphs are well-established, spectral
theory for hypergraphs remains an active area of research. In this paper, we
use random walks to develop a spectral theory for hypergraphs with
edge-dependent vertex weights: hypergraphs where every vertex has a weight
for each incident hyperedge that describes the contribution
of to the hyperedge . We derive a random walk-based hypergraph
Laplacian, and bound the mixing time of random walks on such hypergraphs.
Moreover, we give conditions under which random walks on such hypergraphs are
equivalent to random walks on graphs. As a corollary, we show that current
machine learning methods that rely on Laplacians derived from random walks on
hypergraphs with edge-independent vertex weights do not utilize higher-order
relationships in the data. Finally, we demonstrate the advantages of
hypergraphs with edge-dependent vertex weights on ranking applications using
real-world datasets.Comment: Accepted to ICML 201
Orbital selective crossover and Mott transitions in an asymmetric Hubbard model of cold atoms in optical lattices
We study the asymmetric Hubbard model at half-filling as a generic model to
describe the physics of two species of repulsively interacting fermionic cold
atoms in optical lattices. We use Dynamical Mean Field Theory to obtain the
paramagnetic phase diagram of the model as function of temperature, interaction
strength and hopping asymmetry. A Mott transition with a region of two
coexistent solutions is found for all nonzero values of the hopping asymmetry.
At low temperatures the metallic phase is a heavy Fermi-liquid, qualitatively
analogous to the Fermi liquid state of the symmetric Hubbard model. Above a
coherence temperature, an orbital-selective crossover takes place, wherein one
fermionic species effectively localizes, and the resulting bad metallic state
resembles the non-Fermi liquid state of the Falicov-Kimball model. We compute
observables relevant to cold atom systems such as the double occupation, the
specific heat and entropy and characterize their behavior in the different
phases
Weak coupling study of decoherence of a qubit in disordered magnetic environments
We study the decoherence of a qubit weakly coupled to frustrated spin baths.
We focus on spin-baths described by the classical Ising spin glass and the
quantum random transverse Ising model which are known to have complex
thermodynamic phase diagrams as a function of an external magnetic field and
temperature. Using a combination of numerical and analytical methods, we show
that for baths initally in thermal equilibrium, the resulting decoherence is
highly sensitive to the nature of the coupling to the environment and is
qualitatively different in different parts of the phase diagram. We find an
unexpected strong non-Markovian decay of the coherence when the random
transverse Ising model bath is prepared in an initial state characterized by a
finite temperature paramagnet. This is contrary to the usual case of
exponential decay (Markovian) expected for spin baths in finite temperature
paramagnetic phases, thereby illustrating the importance of the underlying
non-trivial dynamics of interacting quantum spinbaths.Comment: 12 pages, 18 figure
Phase diagram of the asymmetric Hubbard model and an entropic chromatographic method for cooling cold fermions in optical lattices
We study the phase diagram of the asymmetric Hubbard model (AHM), which is
characterized by different values of the hopping for the two spin projections
of a fermion or equivalently, two different orbitals. This model is expected to
provide a good description of a mass-imbalanced cold fermionic mixture in a 3D
optical lattice. We use the dynamical mean field theory to study various
physical properties of this system. In particular, we show how
orbital-selective physics, observed in multi-orbital strongly correlated
electron systems, can be realized in such a simple model. We find that the
density distribution is a good probe of this orbital selective crossover from a
Fermi liquid to a non-Fermi liquid state.
Below an ordering temperature , which is a function of both the
interaction and hopping asymmetry, the system exhibits staggered long range
orbital order. Apart from the special case of the symmetric limit, i.e.,
Hubbard model, where there is no hopping asymmetry, this orbital order is
accompanied by a true charge density wave order for all values of the hopping
asymmetry. We calculate the order parameters and various physical quantities
including the thermodynamics in both the ordered and disordered phases. We find
that the formation of the charge density wave is signaled by an abrupt increase
in the sublattice double occupancies. Finally, we propose a new method,
entropic chromatography, for cooling fermionic atoms in optical lattices, by
exploiting the properties of the AHM. To establish this cooling strategy on a
firmer basis, we also discuss the variations in temperature induced by the
adiabatic tuning of interactions and hopping parameters.Comment: 16 pages, 19 fig
Effective action approach to strongly correlated fermion systems
We construct a new functional for the single particle Green's function, which
is a variant of the standard Baym Kadanoff functional.
The stability of the stationary solutions to the new functional is directly
related to aspects of the irreducible particle hole interaction through the
Bethe Salpeter equation.
A startling aspect of this functional is that it allows a simple and rigorous
derivation of both the standard and extended dynamical mean field (DMFT)
equations as stationary conditions. Though the DMFT equations were formerly
obtained only in the limit of infinite lattice coordination, the new functional
described in the work, presents a way of directly extending DMFT to finite
dimensional systems, both on a lattice and in a continuum. Instabilities of the
stationary solution at the bifurcation point of the functional, signal the
appearance of a zero mode at the Mott transition which then couples t o
physical quantities resulting in divergences at the transition.Comment: 9 page
Superlattice switching from parametric instabilities in a driven-dissipative BEC in a cavity
We numerically obtain the full time-evolution of a parametrically-driven
dissipative Bose-Einstein condensate in an optical cavity and investigate the
implications of driving for the phase diagram. Beyond the normal and
superradiant phases, a third nonequilibrium phase emerges as a manybody
parametric resonance. This dynamical normal phase switches between two
symmetry-broken superradiant configurations. The switching implies a breakdown
of the system's mapping to the Dicke model. Unlike the other phases, the
dynamical normal phase shows features of nonintegrability and thermalization.Comment: 5 pages, 3 figure
Impurity effects in the quantum kagome system ZnCu3(OH)6Cl2
Motivated by the recent experiments on the new spin half Kagome compound
ZnCu3(OH)6Cl2, we study a phenomenological model of a frustrated quantum
magnet. The model has a spin liquid groundstate and is constructed so as to
mimic the macroscopically large quasi-degeneracies expected in the low-lying
energy structure of a Kagome system. We use numerical studies of finite size
systems to investigate the static as well as the dynamical response at finite
temperatures. The results obtained using our simple model are compatible with a
large number of recent experiments including neutron scattering data. Our study
suggests that many of the anomalous features observed in experiments have a
natural interpretation in terms of a spin-1/2 defects (impurities) coupled to
an underlying Kagome-type spin liquid.Comment: text+5fig
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