16,974 research outputs found
Critical Entanglement for the Half-Filled Extended Hubbard Model
We study the ground state of the one-dimensional extended Hubbard model at
half-filling using the entanglement entropy calculated by Density Matrix
Renormalization Group (DMRG) techniques. We apply a novel curve fitting and
scaling method to accurately identify a order critical point as well
as a Berezinskii-Kosterlitz-Thouless (BKT) critical point. Using open boundary
conditions and medium-sized lattices with very small truncation errors, we are
able to achieve similar accuracy to previous authors. We also report
observations of finite-size and boundary effects that can be remedied with
careful pinning.Comment: 10 pages, 12 figure
Optimal Sensor Collaboration for Parameter Tracking Using Energy Harvesting Sensors
In this paper, we design an optimal sensor collaboration strategy among
neighboring nodes while tracking a time-varying parameter using wireless sensor
networks in the presence of imperfect communication channels. The sensor
network is assumed to be self-powered, where sensors are equipped with energy
harvesters that replenish energy from the environment. In order to minimize the
mean square estimation error of parameter tracking, we propose an online sensor
collaboration policy subject to real-time energy harvesting constraints. The
proposed energy allocation strategy is computationally light and only relies on
the second-order statistics of the system parameters. For this, we first
consider an offline non-convex optimization problem, which is solved exactly
using semidefinite programming. Based on the offline solution, we design an
online power allocation policy that requires minimal online computation and
satisfies the dynamics of energy flow at each sensor. We prove that the
proposed online policy is asymptotically equivalent to the optimal offline
solution and show its convergence rate and robustness. We empirically show that
the estimation performance of the proposed online scheme is better than that of
the online scheme when channel state information about the dynamical system is
available in the low SNR regime. Numerical results are conducted to demonstrate
the effectiveness of our approach
Dominant Superconducting Fluctuations in the One-Dimensional Extended Holstein-Extended Hubbard model
The search for realistic one-dimensional (1D) models that exhibit dominant
superconducting (SC) fluctuations effects has a long history. In these 1D
systems, the effects of commensurate band fillings--strongest at
half-filling--and electronic repulsions typically lead to a finite charge gap
and the favoring of insulating density wave ordering over superconductivity.
Accordingly, recent proposals suggesting a gapless metallic state in the
Holstein-Hubbard (HH) model, possibly superconducting, have generated
considerable interest and controversy, with the most recent work demonstrating
that the putative dominant superconducting state likely does not exist. In this
paper we study a model with non-local electron-phonon interactions, in addition
to electron-electron interactions, this model unambiguously possesses dominant
superconducting fluctuations at half filling in a large region of parameter
space. Using both the numerical multi-scale functional renormalization group
for the full model and an analytic conventional renormalization group for a
bosonized version of the model, we demonstrate the existence of dominant
superconducting (SC) fluctuations. These dominant SC fluctuations arise because
the spin-charge coupling at high energy is weakened by the non-local
electron-phonon interaction and the charge gap is destroyed by the resultant
suppression of the Umklapp process. The existence of the dominant SC pairing
instability in this half-filled 1D system suggests that non-local
boson-mediated interactions may be important in the superconductivity observed
in the organic superconductors.Comment: 8 pages, 4 figure
Functional renormalization group analysis of the half-filled one-dimensional extended Hubbard model
We study the phase diagram of the half-filled one-dimensional extended Hubbard model at weak coupling using a novel functional renormalization group (FRG) approach. The FRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi points. Our results confirm the existence of a finite region of bond charge density wave, also known as a "bond order wave" near U=2V and clarify why earlier g-ology calculations have not found this phase. We argue that this is an example in which formally irrelevant corrections change the topology of the phase diagram. Whenever marginal terms lead to an accidental symmetry, this generalized FRG method may be crucial to characterize the phase diagram accurately.First author draf
A Probabilistic Linear Genetic Programming with Stochastic Context-Free Grammar for solving Symbolic Regression problems
Traditional Linear Genetic Programming (LGP) algorithms are based only on the
selection mechanism to guide the search. Genetic operators combine or mutate
random portions of the individuals, without knowing if the result will lead to
a fitter individual. Probabilistic Model Building Genetic Programming (PMB-GP)
methods were proposed to overcome this issue through a probability model that
captures the structure of the fit individuals and use it to sample new
individuals. This work proposes the use of LGP with a Stochastic Context-Free
Grammar (SCFG), that has a probability distribution that is updated according
to selected individuals. We proposed a method for adapting the grammar into the
linear representation of LGP. Tests performed with the proposed probabilistic
method, and with two hybrid approaches, on several symbolic regression
benchmark problems show that the results are statistically better than the
obtained by the traditional LGP.Comment: Genetic and Evolutionary Computation Conference (GECCO) 2017, Berlin,
German
Global Entanglement for Multipartite Quantum States
Based on the residual entanglement [9] (Phys. Rev. A \textbf{71}, 044301
(2005)), we present the global entanglement for a multipartite quantum state.
The measure is shown to be also obtained by the bipartite partitions of the
multipartite state. The distinct characteristic of the global entanglement is
that it consists of the sum of different entanglement contributions. The
measure can provide sufficient and necessary condition of fully separability
for pure states and be conveniently extended to mixed states by minimizing the
convex hull. To test the sufficiency of the measure for mixed states, we
evaluate the global entanglement of bound entangled states. The properties of
the measure discussed finally show the global entanglement is an entanglement
monotone.Comment: 6 page
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