7,131 research outputs found
Neural-Network Quantum States, String-Bond States, and Chiral Topological States
Neural-Network Quantum States have been recently introduced as an Ansatz for
describing the wave function of quantum many-body systems. We show that there
are strong connections between Neural-Network Quantum States in the form of
Restricted Boltzmann Machines and some classes of Tensor-Network states in
arbitrary dimensions. In particular we demonstrate that short-range Restricted
Boltzmann Machines are Entangled Plaquette States, while fully connected
Restricted Boltzmann Machines are String-Bond States with a nonlocal geometry
and low bond dimension. These results shed light on the underlying architecture
of Restricted Boltzmann Machines and their efficiency at representing many-body
quantum states. String-Bond States also provide a generic way of enhancing the
power of Neural-Network Quantum States and a natural generalization to systems
with larger local Hilbert space. We compare the advantages and drawbacks of
these different classes of states and present a method to combine them
together. This allows us to benefit from both the entanglement structure of
Tensor Networks and the efficiency of Neural-Network Quantum States into a
single Ansatz capable of targeting the wave function of strongly correlated
systems. While it remains a challenge to describe states with chiral
topological order using traditional Tensor Networks, we show that
Neural-Network Quantum States and their String-Bond States extension can
describe a lattice Fractional Quantum Hall state exactly. In addition, we
provide numerical evidence that Neural-Network Quantum States can approximate a
chiral spin liquid with better accuracy than Entangled Plaquette States and
local String-Bond States. Our results demonstrate the efficiency of neural
networks to describe complex quantum wave functions and pave the way towards
the use of String-Bond States as a tool in more traditional machine-learning
applications.Comment: 15 pages, 7 figure
Non-equilibrium dynamics of stochastic point processes with refractoriness
Stochastic point processes with refractoriness appear frequently in the
quantitative analysis of physical and biological systems, such as the
generation of action potentials by nerve cells, the release and reuptake of
vesicles at a synapse, and the counting of particles by detector devices. Here
we present an extension of renewal theory to describe ensembles of point
processes with time varying input. This is made possible by a representation in
terms of occupation numbers of two states: Active and refractory. The dynamics
of these occupation numbers follows a distributed delay differential equation.
In particular, our theory enables us to uncover the effect of refractoriness on
the time-dependent rate of an ensemble of encoding point processes in response
to modulation of the input. We present exact solutions that demonstrate generic
features, such as stochastic transients and oscillations in the step response
as well as resonances, phase jumps and frequency doubling in the transfer of
periodic signals. We show that a large class of renewal processes can indeed be
regarded as special cases of the model we analyze. Hence our approach
represents a widely applicable framework to define and analyze non-stationary
renewal processes.Comment: 8 pages, 4 figure
Nonlocal effects on magnetism in the diluted magnetic semiconductor Ga_{1-x}Mn_{x}As
The magnetic properties of the diluted magnetic semiconductor
Ga_{1-x}Mn_{x}As are studied within the dynamical cluster approximation. We use
the k-dot-p Hamiltonian to describe the electronic structure of GaAs with
spin-orbit coupling and strain effects. We show that nonlocal effects are
essential for explaining the experimentally observed transition temperature and
saturation magnetization. We also demonstrate that the cluster anisotropy is
very strong and induces rotational frustration and a cube-edge direction
magnetic anisotropy at low temperature. With this, we explain the
temperature-driven spin reorientation in this system.Comment: 4 pages, 4 figures; to be published in Phys. Rev. Let
X-ray structure analysis of the InSb ( )-(3 × 3) reconstruction
The (3 × 3) reconstruction of the InSb( ) surface has been analysed using grazing incidence X-ray diffraction. The reconstruction is characterized by hexamers above a complete InSb double-layer centred around an Sb atom. No vacancies are found in the structure as predicted theoretically. The results agree with scanning tunnelling microscopy measurements
Pesin's Formula for Random Dynamical Systems on
Pesin's formula relates the entropy of a dynamical system with its positive
Lyapunov exponents. It is well known, that this formula holds true for random
dynamical systems on a compact Riemannian manifold with invariant probability
measure which is absolutely continuous with respect to the Lebesgue measure. We
will show that this formula remains true for random dynamical systems on
which have an invariant probability measure absolutely continuous to the
Lebesgue measure on . Finally we will show that a broad class of
stochastic flows on of a Kunita type satisfies Pesin's formula.Comment: 35 page
Cu -edge Resonant Inelastic X-Ray Scattering in Edge-Sharing Cuprates
We present calculations for resonant inelastic x-ray scattering (RIXS) in
edge-shared copper oxide systems, such as CuGeO and LiCuO,
appropriate for hard x-ray scattering where the photoexcited electron lies
above oxygen 2p and copper 3d orbital energies. We perform exact
diagonalizations of the multi-band Hubbard and determine the energies, orbital
character and resonance profiles of excitations which can be probed via RIXS.
We find excellent agreement with recent results on LiCuO and
CuGeO in the 2-7 eV photon energy loss range.Comment: Updated with new data, expanded 9 pages, 9 figure
Adsorption induced reconstruction of the Cu(110) surface
The formation of the O/Cu(110)-(2 × 1) and H/Cu(110)-(1 × 2) superstructures has been investigated by a LEED beam profile analysis. The oxygen induced reconstruction proceeds at later stages by creation of holes on flat terraces. This could not be observed at the hydrogen induced missing row reconstruction. The formation of the missing row structure proceeds most probably via nucleation at steps and subsequent growth of (1 × 2) islands. The influence of different distributions of steps and islands on beam profiles is discussed
Orbital Order and Spontaneous Orthorhombicity in Iron Pnictides
A growing list of experiments show orthorhombic electronic anisotropy in the
iron pnictides, in some cases at temperatures well above the spin density wave
transition. These experiments include neutron scattering, resistivity and
magnetoresistance measurements, and a variety of spectroscopies. We explore the
idea that these anisotropies stem from a common underlying cause: orbital order
manifest in an unequal occupation of and orbitals, arising
from the coupled spin-orbital degrees of freedom. We emphasize the distinction
between the total orbital occupation (the integrated density of states), where
the order parameter may be small, and the orbital polarization near the Fermi
level which can be more pronounced. We also discuss light-polarization studies
of angle-resolved photoemission, and demonstrate how x-ray absorption linear
dichroism may be used as a method to detect an orbital order parameter.Comment: Orig.: 4+ pages; Rev.: 4+ pages with updated content and reference
Surface Geometry of C60 on Ag(111)
The geometry of adsorbed C60 influences its collective properties. We report the first dynamical low-energy electron diffraction study to determine the geometry of a C60 monolayer, Ag(111)-(23×23)30°-C60, and related density functional theory calculations. The stable monolayer has C60 molecules in vacancies that result from the displacement of surface atoms. C60 bonds with hexagons down, with their mirror planes parallel to that of the substrate. The results indicate that vacancy structures are the rule rather than the exception for C60 monolayers on close-packed metal surfaces. © 2009 The American Physical Society
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