7,093 research outputs found
Matrix product decomposition and classical simulation of quantum dynamics in the presence of a symmetry
We propose a refined matrix product state representation for many-body
quantum states that are invariant under SU(2) transformations, and indicate how
to extend the time-evolving block decimation (TEBD) algorithm in order to
simulate time evolution in an SU(2) invariant system. The resulting algorithm
is tested in a critical quantum spin chain and shown to be significantly more
efficient than the standard TEBD.Comment: 5 pages, 4 figure
Quantifying Quantum Correlations in Fermionic Systems using Witness Operators
We present a method to quantify quantum correlations in arbitrary systems of
indistinguishable fermions using witness operators. The method associates the
problem of finding the optimal entan- glement witness of a state with a class
of problems known as semidefinite programs (SDPs), which can be solved
efficiently with arbitrary accuracy. Based on these optimal witnesses, we
introduce a measure of quantum correlations which has an interpretation
analogous to the Generalized Robust- ness of entanglement. We also extend the
notion of quantum discord to the case of indistinguishable fermions, and
propose a geometric quantifier, which is compared to our entanglement measure.
Our numerical results show a remarkable equivalence between the proposed
Generalized Robustness and the Schliemann concurrence, which are equal for pure
states. For mixed states, the Schliemann con- currence presents itself as an
upper bound for the Generalized Robustness. The quantum discord is also found
to be an upper bound for the entanglement.Comment: 7 pages, 6 figures, Accepted for publication in Quantum Information
Processin
Tensor network states and geometry
Tensor network states are used to approximate ground states of local
Hamiltonians on a lattice in D spatial dimensions. Different types of tensor
network states can be seen to generate different geometries. Matrix product
states (MPS) in D=1 dimensions, as well as projected entangled pair states
(PEPS) in D>1 dimensions, reproduce the D-dimensional physical geometry of the
lattice model; in contrast, the multi-scale entanglement renormalization ansatz
(MERA) generates a (D+1)-dimensional holographic geometry. Here we focus on
homogeneous tensor networks, where all the tensors in the network are copies of
the same tensor, and argue that certain structural properties of the resulting
many-body states are preconditioned by the geometry of the tensor network and
are therefore largely independent of the choice of variational parameters.
Indeed, the asymptotic decay of correlations in homogeneous MPS and MERA for
D=1 systems is seen to be determined by the structure of geodesics in the
physical and holographic geometries, respectively; whereas the asymptotic
scaling of entanglement entropy is seen to always obey a simple boundary law --
that is, again in the relevant geometry. This geometrical interpretation offers
a simple and unifying framework to understand the structural properties of, and
helps clarify the relation between, different tensor network states. In
addition, it has recently motivated the branching MERA, a generalization of the
MERA capable of reproducing violations of the entropic boundary law in D>1
dimensions.Comment: 18 pages, 18 figure
Entanglement Perturbation Theory for Antiferromagnetic Heisenberg Spin Chains
A recently developed numerical method, entanglement perturbation theory
(EPT), is used to study the antiferromagnetic Heisenberg spin chains with
z-axis anisotropy and magnetic field B. To demonstrate the accuracy,
we first apply EPT to the isotropic spin-1/2 antiferromagnetic Heisenberg
model, and find that EPT successfully reproduces the exact Bethe Ansatz results
for the ground state energy, the local magnetization, and the spin correlation
functions (Bethe ansatz result is available for the first 7 lattice
separations). In particular, EPT confirms for the first time the asymptotic
behavior of the spin correlation functions predicted by the conformal field
theory, which realizes only for lattice separations larger than 1000. Next,
turning on the z-axis anisotropy and the magnetic field, the 2-spin and 4-spin
correlation functions are calculated, and the results are compared with those
obtained by Bosonization and density matrix renormalization group methods.
Finally, for the spin-1 antiferromagnetic Heisenberg model, the ground state
phase diagram in space is determined with help of the Roomany-Wyld RG
finite-size-scaling. The results are in good agreement with those obtained by
the level-spectroscopy method.Comment: 12 pages, 14 figure
From the discrete to the continuous - towards a cylindrically consistent dynamics
Discrete models usually represent approximations to continuum physics.
Cylindrical consistency provides a framework in which discretizations mirror
exactly the continuum limit. Being a standard tool for the kinematics of loop
quantum gravity we propose a coarse graining procedure that aims at
constructing a cylindrically consistent dynamics in the form of transition
amplitudes and Hamilton's principal functions. The coarse graining procedure,
which is motivated by tensor network renormalization methods, provides a
systematic approximation scheme towards this end. A crucial role in this coarse
graining scheme is played by embedding maps that allow the interpretation of
discrete boundary data as continuum configurations. These embedding maps should
be selected according to the dynamics of the system, as a choice of embedding
maps will determine a truncation of the renormalization flow.Comment: 22 page
Hard Two-Photon Contribution to Elastic Lepton-Proton Scattering: Determined by the OLYMPUS Experiment
The OLYMPUS collaboration reports on a precision measurement of the
positron-proton to electron-proton elastic cross section ratio, ,
a direct measure of the contribution of hard two-photon exchange to the elastic
cross section. In the OLYMPUS measurement, 2.01~GeV electron and positron beams
were directed through a hydrogen gas target internal to the DORIS storage ring
at DESY. A toroidal magnetic spectrometer instrumented with drift chambers and
time-of-flight scintillators detected elastically scattered leptons in
coincidence with recoiling protons over a scattering angle range of to . The relative luminosity between the two beam species
was monitored using tracking telescopes of interleaved GEM and MWPC detectors
at , as well as symmetric M{\o}ller/Bhabha calorimeters at
. A total integrated luminosity of 4.5~fb was collected. In
the extraction of , radiative effects were taken into account
using a Monte Carlo generator to simulate the convolutions of internal
bremsstrahlung with experiment-specific conditions such as detector acceptance
and reconstruction efficiency. The resulting values of , presented
here for a wide range of virtual photon polarization ,
are smaller than some hadronic two-photon exchange calculations predict, but
are in reasonable agreement with a subtracted dispersion model and a
phenomenological fit to the form factor data.Comment: 5 pages, 3 figures, 2 table
Out-of-equilibrium physics in driven dissipative coupled resonator arrays
Coupled resonator arrays have been shown to exhibit interesting many- body
physics including Mott and Fractional Hall states of photons. One of the main
differences between these photonic quantum simulators and their cold atoms
coun- terparts is in the dissipative nature of their photonic excitations. The
natural equi- librium state is where there are no photons left in the cavity.
Pumping the system with external drives is therefore necessary to compensate
for the losses and realise non-trivial states. The external driving here can
easily be tuned to be incoherent, coherent or fully quantum, opening the road
for exploration of many body regimes beyond the reach of other approaches. In
this chapter, we review some of the physics arising in driven dissipative
coupled resonator arrays including photon fermionisa- tion, crystallisation, as
well as photonic quantum Hall physics out of equilibrium. We start by briefly
describing possible experimental candidates to realise coupled resonator arrays
along with the two theoretical models that capture their physics, the
Jaynes-Cummings-Hubbard and Bose-Hubbard Hamiltonians. A brief review of the
analytical and sophisticated numerical methods required to tackle these systems
is included.Comment: Chapter that appeared in "Quantum Simulations with Photons and
Polaritons: Merging Quantum Optics with Condensed Matter Physics" edited by
D.G.Angelakis, Quantum Science and Technology Series, Springer 201
Evaluation of turbulent dissipation rate retrievals from Doppler Cloud Radar
Turbulent dissipation rate retrievals from cloud radar Doppler velocity measurements are evaluated using independent, in situ observations in Arctic stratocumulus clouds. In situ validation data sets of dissipation rate are derived using sonic anemometer measurements from a tethered balloon and high frequency pressure variation observations from a research aircraft, both flown in proximity to stationary, ground-based radars. Modest biases are found among the data sets in particularly low- or high-turbulence regimes, but in general the radar-retrieved values correspond well with the in situ measurements. Root mean square differences are typically a factor of 4-6 relative to any given magnitude of dissipation rate. These differences are no larger than those found when comparing dissipation rates computed from tetheredballoon and meteorological tower-mounted sonic anemometer measurements made at spatial distances of a few hundred meters. Temporal lag analyses suggest that approximately half of the observed differences are due to spatial sampling considerations, such that the anticipated radar-based retrieval uncertainty is on the order of a factor of 2-3. Moreover, radar retrievals are clearly able to capture the vertical dissipation rate structure observed by the in situ sensors, while offering substantially more information on the time variability of turbulence profiles. Together these evaluations indicate that radar-based retrievals can, at a minimum, be used to determine the vertical structure of turbulence in Arctic stratocumulus clouds
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