1,555 research outputs found
On single-copy entanglement
The largest eigenvalue of the reduced density matrix for quantum chains is
shown to have a simple physical interpretation and power-law behaviour in
critical systems. This is verified numerically for XXZ spin chains.Comment: 4 pages, 2 figures, note added, typo correcte
On the reduced density matrix for a chain of free electrons
The properties of the reduced density matrix describing an interval of N
sites in an infinite chain of free electrons are investigated. A commuting
operator is found for arbitrary filling and also for open chains. For a half
filled periodic chain it is used to determine the eigenfunctions for the
dominant eigenvalues analytically in the continuum limit. Relations to the
critical six-vertex model are discussed.Comment: 8 pages, small changes, Equ.(24) corrected, final versio
On entanglement evolution across defects in critical chains
We consider a local quench where two free-fermion half-chains are coupled via
a defect. We show that the logarithmic increase of the entanglement entropy is
governed by the same effective central charge which appears in the ground-state
properties and which is known exactly. For unequal initial filling of the
half-chains, we determine the linear increase of the entanglement entropy.Comment: 11 pages, 5 figures, minor changes, reference adde
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
Ising films with surface defects
The influence of surface defects on the critical properties of magnetic films
is studied for Ising models with nearest-neighbour ferromagnetic couplings. The
defects include one or two adjacent lines of additional atoms and a step on the
surface. For the calculations, both density-matrix renormalization group and
Monte Carlo techniques are used. By changing the local couplings at the defects
and the film thickness, non-universal features as well as interesting crossover
phenomena in the magnetic exponents are observed.Comment: 8 pages, 12 figures included, submitted to European Physical Journal
On reduced density matrices for disjoint subsystems
We show that spin and fermion representations for solvable quantum chains
lead in general to different reduced density matrices if the subsystem is not
singly connected. We study the effect for two sites in XX and XY chains as well
as for sublattices in XX and transverse Ising chains.Comment: 10 pages, 4 figure
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
Density-Matrix Spectra of Solvable Fermionic Systems
We consider non-interacting fermions on a lattice and give a general result
for the reduced density matrices corresponding to parts of the system. This
allows to calculate their spectra, which are essential in the DMRG method, by
diagonalizing small matrices. We discuss these spectra and their typical
features for various fermionic quantum chains and for the two-dimensional
tight-binding model.Comment: 12 pages and 9 figure
Qualitative Analysis of Nonlinear Systems by the Lotka-Volterra Approach
In this paper, the authors summarize recent results obtained by applying the Lotka-Volterra approach to problems in nonlinear systems analysis. This approach was developed at the Mathematics and Cybernetics Division of the GDR Academy of Sciences (Berlin); various applications have been investigated in collaboration with the System and Decision Sciences Program at IIASA.
This paper should also be seen as a contribution to the debate on future directions of research at IIASA, in particular possible research into the evolution of macrosystems
- …