1,531 research outputs found
Critical Properties of the One-Dimensional Forest-Fire Model
The one-dimensional forest-fire model including lightnings is studied
numerically and analytically. For the tree correlation function, a new
correlation length with critical exponent \nu ~ 5/6 is found by simulations. A
Hamiltonian formulation is introduced which enables one to study the stationary
state close to the critical point using quantum-mechanical perturbation theory.
With this formulation also the structure of the low-lying relaxation spectrum
and the critical behaviour of the smallest complex gap are investigated
numerically. Finally, it is shown that critical correlation functions can be
obtained from a simplified model involving only the total number of trees
although such simplified models are unable to reproduce the correct
off-critical behaviour.Comment: 24 pages (plain TeX), 4 PostScript figures, uses psfig.st
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
Temperature driven crossover phenomena in the correlation lengths of the one-dimensional t-J model
We describe a modified transfer matrix renormalization group (TMRG) algorithm
and apply it to calculate thermodynamic properties of the one-dimensional t-J
model. At the supersymmetric point we compare with Bethe ansatz results and
make direct connection to conformal field theory (CFT). In particular we study
the crossover from the non-universal high T lattice into the quantum critical
regime by calculating various correlation lengths and static correlation
functions. Finally, the existence of a spin-gap phase is confirmed.Comment: 7 pages, 7 figure
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
Optical Zener-Bloch oscillations in binary waveguide arrays
Zener tunneling in a binary array of coupled optical waveguides with
transverse index gradient is shown to produce a sequence of regular or
irregular beam splitting and beam recombination events superimposed to Bloch
oscillations. These periodic or aperiodic Zener-Bloch oscillations provide a
clear and visualizable signature in an optical system of coherent multiband
dynamics encountered in solid-state or matter-wave system
On the relation between entanglement and subsystem Hamiltonians
We show that a proportionality between the entanglement Hamiltonian and the
Hamiltonian of a subsystem exists near the limit of maximal entanglement under
certain conditions. Away from that limit, solvable models show that the
coupling range differs in both quantities and allow to investigate the effect.Comment: 7 pages, 2 figures version2: minor changes, typos correcte
Discrete gap solitons in modulated waveguide arrays
We suggest a novel concept of diffraction management in waveguide arrays and
predict the existence of discrete gap solitons that possess the properties of
both conventional discrete and Bragg grating solitons. We demonstrate that both
the soliton velocity and propagation direction can be controlled by varying the
input light intensity.Comment: 4 pages, 3 figure
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
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
- …