226 research outputs found
Lightcone renormalization and quantum quenches in one-dimensional Hubbard models
The Lieb-Robinson bound implies that the unitary time evolution of an
operator can be restricted to an effective light cone for any Hamiltonian with
short-range interactions. Here we present a very efficient renormalization
group algorithm based on this light cone structure to study the time evolution
of prepared initial states in the thermodynamic limit in one-dimensional
quantum systems. The algorithm does not require translational invariance and
allows for an easy implementation of local conservation laws. We use the
algorithm to investigate the relaxation dynamics of double occupancies in
fermionic Hubbard models as well as a possible thermalization. For the
integrable Hubbard model we find a pure power-law decay of the number of doubly
occupied sites towards the value in the long-time limit while the decay becomes
exponential when adding a nearest neighbor interaction. In accordance with the
eigenstate thermalization hypothesis, the long-time limit is reasonably well
described by a thermal average. We point out though that such a description
naturally requires the use of negative temperatures. Finally, we study a
doublon impurity in a N\'eel background and find that the excess charge and
spin spread at different velocities, providing an example of spin-charge
separation in a highly excited state.Comment: published versio
Is local scale invariance a generic property of ageing phenomena ?
In contrast to recent claims by Enss, Henkel, Picone, and Schollwoeck [J.
Phys. A 37, 10479] it is shown that the critical autoresponse function of the
1+1-dimensional contact process is not in agreement with the predictions of
local scale invariance.Comment: 7 pages, 3 figures, final form, c++ source code on reques
Magnetic Field Dependent Tunneling in Glasses
We report on experiments giving evidence for quantum effects of
electromagnetic flux in barium alumosilicate glass. In contrast to expectation,
below 100 mK the dielectric response becomes sensitive to magnetic fields. The
experimental findings include both, the complete lifting of the dielectric
saturation by weak magnetic fields and oscillations of the dielectric response
in the low temperature resonant regime. As origin of these effects we suggest
that the magnetic induction field violates the time reversal invariance leading
to a flux periodicity in the energy levels of tunneling systems. At low
temperatures, this effect is strongly enhanced by the interaction between
tunneling systems and thus becomes measurable.Comment: 4 pages, 4 figure
Electron energy relaxation by phonons in the Kondo condensate
We have used normal metal-insulator-superconductor tunnel junctions as
thermometers at sub-Kelvin temperatures to study the electron-phonon (e-p)
interaction in thin Aluminum films doped with Manganese, as a function of
Manganese concentration. Mn in Al is known to be a Kondo impurity with
extremely high Kondo temperature 500 K, thus our results probe the
e-p coupling in the fully spin compensated, unitary limit. The temperature
dependence of the e-p interaction is consistent with the existing theory for
disordered metals, however full theory including the Kondo effect has not been
worked out yet. The strength of the interaction decreases with increasing
Manganese concentration, providing a means to improve sensitivity of detectors
and efficiency of solid state coolers
Evidence for a Second Order Phase Transition in Glasses at Very Low Temperatures -- A Macroscopic Quantum State of Tunneling Systems
Dielectric measurements at very low temperature indicate that in a glass with
the eutectic composition BaO-AlO-SiO a phase transition occurs at
5.84 mK. Below that temperature small magnetic fields of the order of 10 T
cause noticeable changes of the dielectric constant although the glass is
insensitive to fields up to 20 T above 10 mK. The experimental findings may be
interpreted as the signature of the formation of a new phase in which many
tunneling systems perform a coherent motion resulting in a macroscopic wave
function.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let
Weakly regular Floquet Hamiltonians with pure point spectrum
We study the Floquet Hamiltonian: -i omega d/dt + H + V(t) as depending on
the parameter omega. We assume that the spectrum of H is discrete, {h_m (m =
1..infinity)}, with h_m of multiplicity M_m. and that V is an Hermitian
operator, 2pi-periodic in t. Let J > 0 and set Omega_0 = [8J/9,9J/8]. Suppose
that for some sigma > 0: sum_{m,n such that h_m > h_n} mu_{mn}(h_m -
h_n)^(-sigma) < infinity where mu_{mn} = sqrt(min{M_m,M_n)) M_m M_n. We show
that in that case there exist a suitable norm to measure the regularity of V,
denoted epsilon, and positive constants, epsilon_* & delta_*, such that: if
epsilon
|Omega_0| - delta_* epsilon and the Floquet Hamiltonian has a pure point
spectrum for all omega in Omega_infinity.Comment: 35 pages, Latex with AmsAr
On the identification of quasiprimary scaling operators in local scale-invariance
The relationship between physical observables defined in lattice models and
the associated (quasi-)primary scaling operators of the underlying field-theory
is revisited. In the context of local scale-invariance, we argue that this
relationship is only defined up to a time-dependent amplitude and derive the
corresponding generalizations of predictions for two-time response and
correlation functions. Applications to non-equilibrium critical dynamics of
several systems, with a fully disordered initial state and vanishing initial
magnetization, including the Glauber-Ising model, the Frederikson-Andersen
model and the Ising spin glass are discussed. The critical contact process and
the parity-conserving non-equilibrium kinetic Ising model are also considered.Comment: 12 pages, Latex2e with IOP macros, 2 figures included; final for
Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit
We give a thorough Biorthonormal Matrix-Product-State (BMPS) analysis of the
Transfer-Matrix Renormalization-Group (TMRG) for non-Hermitian matrices in the
thermodynamic limit. The BMPS is built on a dual series of reduced
biorthonormal bases for the left and right Perron states of a non-Hermitian
matrix. We propose two alternative infinite-size Biorthonormal TMRG (iBTMRG)
algorithms and compare their numerical performance in both finite and infinite
systems. We show that both iBTMRGs produce a dual infinite-BMPS (iBMPS) which
are translationally invariant in the thermodynamic limit. We also develop an
efficient wave function transformation of the iBTMRG, an analogy of McCulloch
in the infinite-DMRG [arXiv:0804.2509 (2008)], to predict the wave function as
the lattice size is increased. The resulting iBMPS allows for probing bulk
properties of the system in the thermodynamic limit without boundary effects
and allows for reducing the computational cost to be independent of the lattice
size, which are illustrated by calculating the magnetization as a function of
the temperature and the critical spin-spin correlation in the thermodynamic
limit for a 2D classical Ising model.Comment: 14 pages, 9 figure
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