920 research outputs found
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
Reduced density matrix and entanglement entropy of permutationally invariant quantum many-body systems
In this paper we discuss the properties of the reduced density matrix of
quantum many body systems with permutational symmetry and present basic
quantification of the entanglement in terms of the von Neumann (VNE), Renyi and
Tsallis entropies. In particular, we show, on the specific example of the spin
Heisenberg model, how the RDM acquires a block diagonal form with respect
to the quantum number fixing the polarization in the subsystem conservation
of and with respect to the irreducible representations of the
group. Analytical expression for the RDM elements and for the
RDM spectrum are derived for states of arbitrary permutational symmetry and for
arbitrary polarizations. The temperature dependence and scaling of the VNE
across a finite temperature phase transition is discussed and the RDM moments
and the R\'{e}nyi and Tsallis entropies calculated both for symmetric ground
states of the Heisenberg chain and for maximally mixed states.Comment: Festschrift in honor of the 60th birthday of Professor Vladimir
Korepin (11 pages, 5 figures
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 spectra of critical and near-critical systems in one dimension
The entanglement spectrum of a pure state of a bipartite system is the full
set of eigenvalues of the reduced density matrix obtained from tracing out one
part. Such spectra are known in several cases to contain important information
beyond that in the entanglement entropy. This paper studies the entanglement
spectrum for a variety of critical and near-critical quantum lattice models in
one dimension, chiefly by the iTEBD numerical method, which enables both
integrable and non-integrable models to be studied. We find that the
distribution of eigenvalues in the entanglement spectra agrees with an
approximate result derived by Calabrese and Lefevre to an accuracy of a few
percent for all models studied. This result applies whether the correlation
length is intrinsic or generated by the finite matrix size accessible in iTEBD.
For the transverse Ising model, the known exact results for the entanglement
spectrum are used to confirm the validity of the iTEBD approach. For more
general models, no exact result is available but the iTEBD results directly
test the hypothesis that all moments of the reduced density matrix are
determined by a single parameter.Comment: 6 pages, 5 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
Critical behaviour in parabolic geometries
We study two-dimensional systems with boundary curves described by power
laws. Using conformal mappings we obtain the correlations at the bulk critical
point. Three different classes of behaviour are found and explained by scaling
arguments which also apply to higher dimensions. For an Ising system of
parabolic shape the behaviour of the order at the tip is also found.Comment: Old paper, for archiving. 6 pages, 1 figure, epsf, IOP macr
Psychotic disorder, khat abuse and aggressive behavior in Somalia: a case report
The current literature on khat and mental disorders focuses on khat-induced disorders neglecting at large the adverse consequences of co-morbid use on pre-existing disorders. The case of a 32 year old Somali with a delusional disorder and co-morbid khat abuse is presented who killed a man in the
state of paranoid delusions. The psychotic exacerbation prior to this incident was accompanied by an increase of khat intake. Co-morbid khat abuse can lead to the deterioration of psychotic disorders, can facilitate aggressive acts and complicates treatment. The medical and legal system of the countries
where khat use reaches highest levels are not fully prepared to deal with such cases. Further research and the development of adequate prevention and treatment measures is urgently needed.
KEY WORDS: khat, psychosis, co-morbidity, aggression, Somali
On the entanglement entropy for a XY spin chain
The entanglement entropy for the ground state of a XY spin chain is related
to the corner transfer matrices of the triangular Ising model and expressed in
closed form.Comment: 4 pages, 2 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
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