101 research outputs found
Luttinger liquid universality in the time evolution after an interaction quench
We provide strong evidence that the relaxation dynamics of one-dimensional,
metallic Fermi systems resulting out of an abrupt amplitude change of the
two-particle interaction has aspects which are universal in the Luttinger
liquid sense: The leading long-time behavior of certain observables is
described by universal functions of the equilibrium Luttinger liquid parameter
and the renormalized velocity. We analytically derive those functions for the
Tomonaga-Luttinger model and verify our hypothesis of universality by
considering spinless lattice fermions within the framework of the density
matrix renormalization group
Influence of non-magnetic impurities on hole doped two-leg Cu-O Hubbard ladders
We study the influence of non magnetic impurities on the phase diagram of
doped two-leg Hubbard Cu-O ladders. In the absence of impurities this system
posseses d-wave superconducting states and orbital current states depending on
the doping. A single, strong, scatterer modifies its environment locally and
this effect is assessed using a renormalization group analysis. At high doping,
disorder causes intraband instabilities and at low doping it promotes interband
instabilities. In the former case, we extend the boundary conformal field
theory method, developed in the context of single chains, to handle the ladder
problem, and we find exact closed-form analytical expressions for the
correlation functions. This allows us to compute experimentally measurable
local quantities such as the nuclear magnetic resonance line broadenings and
scanning tunnelling microscope profiles. We also discuss the low doping regime
where Kondo physics is at play, making qualitative predictions about its
nature. Insight into collective effects is also given in the many weak
impurities case, based on an RG approach. In this regime, one sees the
interplay between interactions and disorder. We emphasize the influence of the
O atoms on disorder effects both for the single- and for the many-defect
situations.Comment: accepted to be published in NJP special editio
Praktische Oberflächenanalytik. Beiträge zu einem Workshop im Forschungszentrum Karlsruhe vom 9.-11.November 1994
Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians
We introduce several exact models for SU(3) spin chains: (1) a
translationally invariant parent Hamiltonian involving four-site interactions
for the trimer chain, with a three-fold degenerate ground state. We provide
numerical evidence that the elementary excitations of this model transform
under representation 3bar of SU(3) if the original spins of the model transform
under rep. 3. (2) a family of parent Hamiltonians for valence bond solids of
SU(3) chains with spin reps. 6, 10, and 8 on each lattice site. We argue that
of these three models, only the latter two exhibit spinon confinement and a
Haldane gap in the excitation spectrum
Low-energy local density of states of the 1D Hubbard model
We examine the local density of states (DOS) at low energies numerically and
analytically for the Hubbard model in one dimension. The eigenstates represent
separate spin and charge excitations with a remarkably rich structure of the
local DOS in space and energy. The results predict signatures of strongly
correlated excitations in the tunneling probability along finite quantum wires,
such as carbon nanotubes, atomic chains or semiconductor wires in scanning
tunneling spectroscopy (STS) experiments. However, the detailed signatures can
only be partly explained by standard Luttinger liquid theory. In particular, we
find that the effective boundary exponent can be negative in finite wires,
which leads to an increase of the local DOS near the edges in contrast to the
established behavior in the thermodynamic limit.Comment: 6 pages, 4 figures, more information can be found at
http://www.physik.uni-kl.de/eggert/papers/index.htm
On the determinant representations of Gaudin models' scalar products and form factors
We propose alternative determinant representations of certain form factors
and scalar products of states in rational Gaudin models realized in terms of
compact spins. We use alternative pseudo-vacuums to write overlaps in terms of
partition functions with domain wall boundary conditions. Contrarily to
Slavnovs determinant formulas, this construction does not require that any of
the involved states be solutions to the Bethe equations; a fact that could
prove useful in certain non-equilibrium problems. Moreover, by using an
atypical determinant representation of the partition functions, we propose
expressions for the local spin raising and lowering operators form factors
which only depend on the eigenvalues of the conserved charges. These
eigenvalues define eigenstates via solutions of a system of quadratic equations
instead of the usual Bethe equations. Consequently, the current work allows
important simplifications to numerical procedures addressing decoherence in
Gaudin models.Comment: 15 pages, 0 figures, Published versio
A renormalization-group analysis of the interacting resonant level model at finite bias: Generic analytic study of static properties and quench dynamics
Using a real-time renormalization group method we study the minimal model of
a quantum dot dominated by charge fluctuations, the two-lead interacting
resonant level model, at finite bias voltage. We develop a set of RG equations
to treat the case of weak and strong charge fluctuations, together with the
determination of power-law exponents up to second order in the Coulomb
interaction. We derive analytic expressions for the charge susceptibility, the
steady-state current and the conductance in the situation of arbitrary system
parameters, in particular away from the particle-hole symmetric point and for
asymmetric Coulomb interactions. In the generic asymmetric situation we find
that power laws can be observed for the current only as function of the level
position (gate voltage) but not as function of the voltage. Furthermore, we
study the quench dynamics after a sudden switch-on of the level-lead couplings.
The time evolution of the dot occupation and current is governed by exponential
relaxation accompanied by voltage-dependent oscillations and characteristic
algebraic decay.Comment: 24 pages, 13 figures; revised versio
Sub-hertz frequency stabilization of a commercial diode laser
We report ultra-stable locking of a commercially available extended cavity
diode laser to a vibration-insensitive high finesse Fabry-Perot cavity. A servo
bandwidth of 2 MHz is demonstrated. The absolute stability of the diode laser
after locking is measured with a three-cornered-hat method. The resulting Allan
deviation reaches a level of at 1 s, corresponding to only
0.93 Hz linewidth, even without vibration isolation of the reference cavity.Comment: 9 pages, 3 figure
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