1,012 research outputs found
Evolution of entanglement after a local quench
We study free electrons on an infinite half-filled chain, starting in the
ground state with a bond defect. We find a logarithmic increase of the
entanglement entropy after the defect is removed, followed by a slow relaxation
towards the value of the homogeneous chain. The coefficients depend
continuously on the defect strength.Comment: 14 pages, 9 figures, final versio
Calculation of reduced density matrices from correlation functions
It is shown that for solvable fermionic and bosonic lattice systems, the
reduced density matrices can be determined from the properties of the
correlation functions. This provides the simplest way to these quantities which
are used in the density-matrix renormalization group method.Comment: 4 page
Waveguide properties of single subwavelength holes demonstrated with radially and azimuthally polarized light
We investigate the transmission of focused beams through single subwavelength
holes in a silver film. We use radially and azimuthally polarized light,
respectively, to excite higher order waveguide modes as well as to match the
radial symmetry of the aperture geometry. Remarkably, the transmission
properties can be described by a classical waveguide model even for thicknesses
of the silver film as thin as a quarter of a wavelength
Density Matrices for a Chain of Oscillators
We consider chains with an optical phonon spectrum and study the reduced
density matrices which occur in density-matrix renormalization group (DMRG)
calculations. Both for one site and for half of the chain, these are found to
be exponentials of bosonic operators. Their spectra, which are correspondingly
exponential, are determined and discussed. The results for large systems are
obtained from the relation to a two-dimensional Gaussian model.Comment: 15 pages,8 figure
Real-space renormalization group approach for the corner Hamiltonian
We present a real-space renormalization group approach for the corner
Hamiltonian, which is relevant to the reduced density matrix in the density
matrix renormalization group. A set of self-consistent equations that the
renormalized Hamiltonian should satisfy in the thermodynamic limit is also
derived from the fixed point of the recursion relation for the corner
Hamiltonian. We demonstrate the renormalization group algorithm for the
XXZ spin chain and show that the results are consistent with the exact
solution. We further examine the renormalization group for the S=1 Heisenberg
spin chain and then discuss the nature of the eigenvalue spectrum of the corner
Hamiltonian for the non-integrable model.Comment: 7 page
Entanglement evolution after connecting finite to infinite quantum chains
We study zero-temperature XX chains and transverse Ising chains and join an
initially separate finite piece on one or on both sides to an infinite
remainder. In both critical and non-critical systems we find a typical increase
of the entanglement entropy after the quench, followed by a slow decay towards
the value of the homogeneous chain. In the critical case, the predictions of
conformal field theory are verified for the first phase of the evolution, while
at late times a step structure can be observed.Comment: 15 pages, 11 figure
Area law and vacuum reordering in harmonic networks
We review a number of ideas related to area law scaling of the geometric
entropy from the point of view of condensed matter, quantum field theory and
quantum information. An explicit computation in arbitrary dimensions of the
geometric entropy of the ground state of a discretized scalar free field theory
shows the expected area law result. In this case, area law scaling is a
manifestation of a deeper reordering of the vacuum produced by majorization
relations. Furthermore, the explicit control on all the eigenvalues of the
reduced density matrix allows for a verification of entropy loss along the
renormalization group trajectory driven by the mass term. A further result of
our computation shows that single-copy entanglement also obeys area law
scaling, majorization relations and decreases along renormalization group
flows.Comment: 15 pages, 6 figures; typos correcte
Wilson-like real-space renormalization group and low-energy effective spectrum of the XXZ chain in the critical regime
We present a novel real-space renormalization group(RG) for the
one-dimensional XXZ model in the critical regime, reconsidering the role of the
cut-off parameter in Wilson's RG for the Kondo impurity problem. We then
demonstrate the RG calculation for the XXZ chain with the free boundary.
Comparing the hierarchical structure of the obtained low-energy spectrum with
the Bethe ansatz result, we find that the proper scaling dimension is
reproduced as a fixed point of the RG transformation.Comment: 4 pages, 6 figures, typos corrected, final versio
Replica Symmetry Breaking in the Random Replicant Model
We study the statistical mechanics of a model describing the coevolution of
species interacting in a random way. We find that at high competition replica
symmetry is broken. We solve the model in the approximation of one step replica
symmetry breaking and we compare our findings with accurate numerical
simulations.Comment: 12 pages, TeX, 5 postscript figures are avalaible upon request,
submitted to Journal of Physics A: Mathematical and Genera
On the experimental investigation of the electric and magnetic response of a single nano-structure
We demonstrate an experimental method to separately test the optical response
of a single sub-wavelength nano-structure to tailored electric and magnetic
field distributions in the optical domain. For this purpose a highly focused
y-polarized TEM10-mode is used which exhibits spatially separated longitudinal
magnetic and transverse electric field patterns. By displacing a single
sub-wavelength nano-structure, namely a single split-ring resonator (SRR), in
the focal plane, different coupling scenarios can be achieved. It is shown
experimentally that the single split-ring resonator tested here responds
dominantly as an electric dipole. A much smaller but yet statistically
significant magnetic dipole contribution is also measured by investigating the
interaction of a single SRR with a magnetic field component perpendicular to
the SRR plane (which is equivalent to the curl of the electric field) as well
as by analyzing the intensity and polarization distribution of the scattered
light with high spatial resolution. The developed experimental setup as well as
the measurement techniques presented in this paper are a versatile tool to
investigate the optical properties of single sub-wavelength nano-structures.Comment: 19 pages, 9 figures, accepted by Optics Expres
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