31,865 research outputs found
Optimal Capacity of the Blume-Emery-Griffiths perceptron
A Blume-Emery-Griffiths perceptron model is introduced and its optimal
capacity is calculated within the replica-symmetric Gardner approach, as a
function of the pattern activity and the imbedding stability parameter. The
stability of the replica-symmetric approximation is studied via the analogue of
the Almeida-Thouless line. A comparison is made with other three-state
perceptrons.Comment: 10 pages, 8 figure
Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories
We consider the tensors generating matrix product states and density
operators in a spin chain. For pure states, we revise the renormalization
procedure introduced by F. Verstraete et al. in 2005 and characterize the
tensors corresponding to the fixed points. We relate them to the states
possessing zero correlation length, saturation of the area law, as well as to
those which generate ground states of local and commuting Hamiltonians. For
mixed states, we introduce the concept of renormalization fixed points and
characterize the corresponding tensors. We also relate them to concepts like
finite correlation length, saturation of the area law, as well as to those
which generate Gibbs states of local and commuting Hamiltonians. One of the
main result of this work is that the resulting fixed points can be associated
to the boundary theories of two-dimensional topological states, through the
bulk-boundary correspondence introduced by Cirac et al. in 2011.Comment: 63 pages, Annals of Physics (2016). Accepted versio
A spherical Hopfield model
We introduce a spherical Hopfield-type neural network involving neurons and
patterns that are continuous variables. We study both the thermodynamics and
dynamics of this model. In order to have a retrieval phase a quartic term is
added to the Hamiltonian. The thermodynamics of the model is exactly solvable
and the results are replica symmetric. A Langevin dynamics leads to a closed
set of equations for the order parameters and effective correlation and
response function typical for neural networks. The stationary limit corresponds
to the thermodynamic results. Numerical calculations illustrate our findings.Comment: 9 pages Latex including 3 eps figures, Addition of an author in the
HTML-abstract unintentionally forgotten, no changes to the manuscrip
Matrix Product State Representations
This work gives a detailed investigation of matrix product state (MPS)
representations for pure multipartite quantum states. We determine the freedom
in representations with and without translation symmetry, derive respective
canonical forms and provide efficient methods for obtaining them. Results on
frustration free Hamiltonians and the generation of MPS are extended, and the
use of the MPS-representation for classical simulations of quantum systems is
discussed.Comment: Minor changes. To appear in QI
Unbounded violations of bipartite Bell Inequalities via Operator Space theory
In this work we show that bipartite quantum states with local Hilbert space
dimension n can violate a Bell inequality by a factor of order (up
to a logarithmic factor) when observables with n possible outcomes are used. A
central tool in the analysis is a close relation between this problem and
operator space theory and, in particular, the very recent noncommutative
embedding theory. As a consequence of this result, we obtain better Hilbert
space dimension witnesses and quantum violations of Bell inequalities with
better resistance to noise
Strong and weak thermalization of infinite non-integrable quantum systems
When a non-integrable system evolves out of equilibrium for a long time,
local observables are expected to attain stationary expectation values,
independent of the details of the initial state. However, intriguing
experimental results with ultracold gases have shown no thermalization in
non-integrable settings, triggering an intense theoretical effort to decide the
question. Here we show that the phenomenology of thermalization in a quantum
system is much richer than its classical counterpart. Using a new numerical
technique, we identify two distinct thermalization regimes, strong and weak,
occurring for different initial states. Strong thermalization, intrinsically
quantum, happens when instantaneous local expectation values converge to the
thermal ones. Weak thermalization, well-known in classical systems, happens
when local expectation values converge to the thermal ones only after time
averaging. Remarkably, we find a third group of states showing no
thermalization, neither strong nor weak, to the time scales one can reliably
simulate.Comment: 12 pages, 21 figures, including additional materia
Stable propagation of pulsed beams in Kerr focusing media with modulated dispersion
We propose the modulation of dispersion to prevent collapse of planar pulsed
beams which propagate in Kerr-type self-focusing optical media. As a result, we
find a new type of two-dimensional spatio-temporal solitons stabilized by
dispersion management. We have studied the existence and properties of these
solitary waves both analytically and numerically. We show that the adequate
choice of the modulation parameters optimizes the stabilization of the pulse.Comment: 3 pages, 3 figures, submitted to Optics Letter
Matrix Product States: Symmetries and Two-Body Hamiltonians
We characterize the conditions under which a translationally invariant matrix
product state (MPS) is invariant under local transformations. This allows us to
relate the symmetry group of a given state to the symmetry group of a simple
tensor. We exploit this result in order to prove and extend a version of the
Lieb-Schultz-Mattis theorem, one of the basic results in many-body physics, in
the context of MPS. We illustrate the results with an exhaustive search of
SU(2)--invariant two-body Hamiltonians which have such MPS as exact ground
states or excitations.Comment: PDFLatex, 12 pages and 6 figure
Parity effects in the scaling of block entanglement in gapless spin chains
We consider the Renyi alpha-entropies for Luttinger liquids (LL). For large
block lengths l these are known to grow like ln l. We show that there are
subleading terms that oscillate with frequency 2k_F (the Fermi wave number of
the LL) and exhibit a universal power-law decay with l. The new critical
exponent is equal to K/(2 alpha), where K is the LL parameter. We present
numerical results for the anisotropic XXZ model and the full analytic solution
for the free fermion (XX) point.Comment: 4 pages, 5 figures. Final version accepted in PR
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