8,531 research outputs found
Dynamical correlation functions of the mesoscopic pairing model
We study the dynamical correlation functions of the Richardson pairing model
(also known as the reduced or discrete-state BCS model) in the canonical
ensemble. We use the Algebraic Bethe Ansatz formalism, which gives exact
expressions for the form factors of the most important observables. By summing
these form factors over a relevant set of states, we obtain very precise
estimates of the correlation functions, as confirmed by global sum-rules
(saturation above 99% in all cases considered). Unlike the case of many other
Bethe Ansatz solvable theories, simple two-particle states are sufficient to
achieve such saturations, even in the thermodynamic limit. We provide explicit
results at half-filling, and discuss their finite-size scaling behavior
Quantum phase transitions in the Kondo-necklace model: Perturbative continuous unitary transformation approach
The Kondo-necklace model can describe magnetic low-energy limit of strongly
correlated heavy fermion materials. There exist multiple energy scales in this
model corresponding to each phase of the system. Here, we study quantum phase
transition between the Kondo-singlet phase and the antiferromagnetic long-range
ordered phase, and show the effect of anisotropies in terms of quantum
information properties and vanishing energy gap. We employ the "perturbative
continuous unitary transformations" approach to calculate the energy gap and
spin-spin correlations for the model in the thermodynamic limit of one, two,
and three spatial dimensions as well as for spin ladders. In particular, we
show that the method, although being perturbative, can predict the expected
quantum critical point, where the gap of low-energy spectrum vanishes, which is
in good agreement with results of other numerical and Green's function
analyses. In addition, we employ concurrence, a bipartite entanglement measure,
to study the criticality of the model. Absence of singularities in the
derivative of concurrence in two and three dimensions in the Kondo-necklace
model shows that this model features multipartite entanglement. We also discuss
crossover from the one-dimensional to the two-dimensional model via the ladder
structure.Comment: 12 pages, 6 figure
Entanglement Entropy of Two Spheres
We study the entanglement entropy S_{AB} of a massless free scalar field on
two spheres A and B whose radii are R_1 and R_2, respectively, and the distance
between the centers of them is r. The state of the massless free scalar field
is the vacuum state. We obtain the result that the mutual information
S_{A;B}:=S_A+S_B-S_{AB} is independent of the ultraviolet cutoff and
proportional to the product of the areas of the two spheres when r>>R_1,R_2,
where S_A and S_B are the entanglement entropy on the inside region of A and B,
respectively. We discuss possible connections of this result with the physics
of black holes.Comment: 17 pages, 9 figures; v4, added references, revised argument in
section V, a typo in eq.(25) corrected, published versio
Thermodynamic entropy of a many body energy eigenstate
It is argued that a typical many body energy eigenstate has a well defined
thermodynamic entropy and that individual eigenstates possess thermodynamic
characteristics analogous to those of generic isolated systems. We examine
large systems with eigenstate energies equivalent to finite temperatures. When
quasi-static evolution of a system is adiabatic (in the quantum mechanical
sense), two coupled subsystems can transfer heat from one subsystem to another
yet remain in an energy eigenstate. To explicitly construct the entropy from
the wave function, degrees of freedom are divided into two unequal parts. It is
argued that the entanglement entropy between these two subsystems is the
thermodynamic entropy per degree of freedom for the smaller subsystem. This is
done by tracing over the larger subsystem to obtain a density matrix, and
calculating the diagonal and off-diagonal contributions to the entanglement
entropy.Comment: 18 page
Dynamical density-density correlations in the one-dimensional Bose gas
The zero-temperature dynamical structure factor of the one-dimensional Bose
gas with delta-function interaction (Lieb-Liniger model) is computed using a
hybrid theoretical/numerical method based on the exact Bethe Ansatz solution,
which allows to interpolate continuously between the weakly-coupled
Thomas-Fermi and strongly-coupled Tonks-Girardeau regimes. The results should
be experimentally accessible with Bragg spectroscopy.Comment: 4 pages, 3 figures, published versio
Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?
We study the time evolution of quantum one-dimensional gapless systems
evolving from initial states with a domain-wall. We generalize the
path-integral imaginary time approach that together with boundary conformal
field theory allows to derive the time and space dependence of general
correlation functions. The latter are explicitly obtained for the Ising
universality class, and the typical behavior of one- and two-point functions is
derived for the general case. Possible connections with the stochastic Loewner
evolution are discussed and explicit results for one-point time dependent
averages are obtained for generic \kappa for boundary conditions corresponding
to SLE. We use this set of results to predict the time evolution of the
entanglement entropy and obtain the universal constant shift due to the
presence of a domain wall in the initial state.Comment: 27 pages, 10 figure
Local scale invariance in the parity conserving nonequilibrium kinetic Ising model
The local scale invariance has been investigated in the nonequilibrium
kinetic Ising model exhibiting absorbing phase transition of PC type in 1+1
dimension. Numerical evidence has been found for the satisfaction of this
symmetry and estimates for the critical ageing exponents are given.Comment: 8 pages, 2 figures (IOP format), final form to appear in JSTA
Entanglement in gapless resonating valence bond states
We study resonating-valence-bond (RVB) states on the square lattice of spins
and of dimers, as well as SU(N)-invariant states that interpolate between the
two. These states are ground states of gapless models, although the
SU(2)-invariant spin RVB state is also believed to be a gapped liquid in its
spinful sector. We show that the gapless behavior in spin and dimer RVB states
is qualitatively similar by studying the R\'enyi entropy for splitting a torus
into two cylinders, We compute this exactly for dimers, showing it behaves
similarly to the familiar one-dimensional log term, although not identically.
We extend the exact computation to an effective theory believed to interpolate
among these states. By numerical calculations for the SU(2) RVB state and its
SU(N)-invariant generalizations, we provide further support for this belief. We
also show how the entanglement entropy behaves qualitatively differently for
different values of the R\'enyi index , with large values of proving a
more sensitive probe here, by virtue of exhibiting a striking even/odd effect.Comment: 44 pages, 14 figures, published versio
Time Evolution within a Comoving Window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains
We present a modification of Matrix Product State time evolution to simulate
the propagation of signal fronts on infinite one-dimensional systems. We
restrict the calculation to a window moving along with a signal, which by the
Lieb-Robinson bound is contained within a light cone. Signal fronts can be
studied unperturbed and with high precision for much longer times than on
finite systems. Entanglement inside the window is naturally small, greatly
lowering computational effort. We investigate the time evolution of the
transverse field Ising (TFI) model and of the S=1/2 XXZ antiferromagnet in
their symmetry broken phases after several different local quantum quenches.
In both models, we observe distinct magnetization plateaus at the signal
front for very large times, resembling those previously observed for the
particle density of tight binding (TB) fermions. We show that the normalized
difference to the magnetization of the ground state exhibits similar scaling
behaviour as the density of TB fermions. In the XXZ model there is an
additional internal structure of the signal front due to pairing, and wider
plateaus with tight binding scaling exponents for the normalized excess
magnetization. We also observe parameter dependent interaction effects between
individual plateaus, resulting in a slight spatial compression of the plateau
widths.
In the TFI model, we additionally find that for an initial Jordan-Wigner
domain wall state, the complete time evolution of the normalized excess
longitudinal magnetization agrees exactly with the particle density of TB
fermions.Comment: 10 pages with 5 figures. Appendix with 23 pages, 13 figures and 4
tables. Largely extended and improved versio
Arsenic contamination at the Bagnoli Bay seabed (South Italy) via particle tracking numerical modeling: Pollution patterns from stationary climatic forcings
Almost 140 years of industrial exploitation have severely degraded the environment of Bagnoli Coroglio (BC), the westernmost neighborhood of the city of Naples (Italy). In this peculiar area, however, geogenic processes overlap with the impact of human activities, making it difficult to distinguish between anthropogenic and geogenic pollution sources. This is particularly true for Arsenic, the concentration of which in the marine sediments largely exceeds the tolerable level for human health and the background value for local pyroclastics. After several studies have used traditional tools based on multivariate statistics, this article attempts at tackling the problem via numerical modeling, which provides a deeper insight into the physics that governs the pollution process. Therefore, we use a particle tracking model to assess whether arsenic levels in the seabed can be affected by the influx of thermal water from an artificial channel outfalling at the westernmost part of the coast The climatic forcings that drive the marine circulation are simplified to basic “scenarios”, in which wind and waves are stationary in strength and direction. Since the simulation time is much less than the contamination timescale, the comparison between numerical results and measurements is essentially qualitative and concerns the shape of contamination contours
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