95 research outputs found
Coexistence of Anomalous and Normal Diffusion in Integrable Mott Insulators
We study the finite-momentum spin dynamics in the one-dimensional XXZ spin
chain within the Ising-type regime at high temperatures using density
autocorrelations within linear response theory and real-time propagation of
nonequilibrium densities. While for the nonintegrable model results are well
consistent with normal diffusion, the finite-size integrable model unveils the
coexistence of anomalous and normal diffusion in different regimes of time. In
particular, numerical results show a Gaussian relaxation at smallest nonzero
momenta which we relate to nonzero stiffness in a grand canonical ensemble. For
larger but still small momenta normal-like diffusion is recovered. Similar
results for the model of impenetrable particles also help to resolve rather
conflicting conclusions on transport in integrable Mott insulators.Comment: 5 pages, 4 figure
Density dynamics from current auto-correlations at finite time- and length-scales
We consider the increase of the spatial variance of some inhomogeneous,
non-equilibrium density (particles, energy, etc.) in a periodic quantum system
of condensed matter-type. This is done for a certain class of initial quantum
states which is supported by static linear response and typicality arguments.
We directly relate the broadening to some current auto-correlation function at
finite times. Our result is not limited to diffusive behavior, however, in that
case it yields a generalized Einstein relation. These findings facilitate the
approximation of diffusion constants/conductivities on the basis of current
auto-correlation functions at finite times for finite systems. Pursuing this,
we quantitatively confirm the magnetization diffusion constant in a spin chain
which was recently found from non-equilibrium bath scenarios.Comment: 4 pages, 1 figure, accepted for publication in Europhys. Let
Eigenstate thermalization within isolated spin-chain systems
The thermalization phenomenon and many-body quantum statistical properties
are studied on the example of several observables in isolated spin-chain
systems, both integrable and generic non-integrable ones. While diagonal matrix
elements for non-integrable models comply with the eigenstate thermalization
hypothesis (ETH), the integrable systems show evident deviations and similarity
to properties of noninteracting many-fermion models. The finite-size scaling
reveals that the crossover between two regimes is given by a scale closely
related to the scattering length. Low-frequency off-diagonal matrix elements
related to d.c. transport quantities in a generic system also follow the
behavior analogous to the ETH, however unrelated to the one of diagonal
elements
Dynamical typicality for initial states with a preset measurement statistics of several commuting observables
We consider all pure or mixed states of a quantum many-body system which
exhibit the same, arbitrary but fixed measurement outcome statistics for
several commuting observables. Taking those states as initial conditions, which
are then propagated by the pertinent Schr\"odinger or von Neumann equation up
to some later time point, and invoking a few additional, fairly weak and
realistic assumptions, we show that most of them still entail very similar
expectation values for any given observable. This so-called dynamical
typicality property thus corroborates the widespread observation that a few
macroscopic features are sufficient to ensure the reproducibility of
experimental measurements despite many unknown and uncontrollable microscopic
details of the system. We also discuss and exemplify the usefulness of our
general analytical result as a powerful numerical tool
Projection operator approach to spin diffusion in the anisotropic Heisenberg chain at high temperatures
We investigate spin transport in the anisotropic Heisenberg chain in the
limit of high temperatures ({\beta} \to 0). We particularly focus on diffusion
and the quantitative evaluation of diffusion constants from current
autocorrelations as a function of the anisotropy parameter {\Delta} and the
spin quantum number s. Our approach is essentially based on an application of
the time-convolutionless (TCL) projection operator technique. Within this
perturbative approach the projection onto the current yields the decay of
autocorrelations to lowest order of {\Delta}. The resulting diffusion constants
scale as 1/{\Delta}^2 in the Markovian regime {\Delta}<<1 (s=1/2) and as
1/{\Delta} in the highly non-Markovian regime above {\Delta} \sim 1 (arbitrary
s). In the latter regime the dependence on s appears approximately as an
overall scaling factor \sqrt{s(s+1)} only. These results are in remarkably good
agreement with diffusion constants for {\Delta}>1 which are obtained directly
from the exact diagonalization of autocorrelations or have been obtained from
non-equilibrium bath scenarios.Comment: 4 pages, 3 figure
Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates
We study trace estimators for equilibrium thermodynamic observables that rely on the idea of typicality and derivatives thereof such as the finite-temperature Lanczos method (FTLM). As numerical examples quantum spin systems are studied. Our initial aim was to identify pathological examples or circumstances, such as strong frustration or unusual densities of states, where these methods could fail. It turned out that all investigated systems allow such approximations. Only at temperatures of the order of the lowest energy gap is the convergence somewhat slower in the number of random vectors over which observables are averaged
Finite-temperature charge transport in the one-dimensional Hubbard model
We study the charge conductivity of the one-dimensional repulsive Hubbard
model at finite temperature using the method of dynamical quantum typicality,
focusing at half filling. This numerical approach allows us to obtain current
autocorrelation functions from systems with as many as 18 sites, way beyond the
range of standard exact diagonalization. Our data clearly suggest that the
charge Drude weight vanishes with a power law as a function of system size. The
low-frequency dependence of the conductivity is consistent with a finite dc
value and thus with diffusion, despite large finite-size effects. Furthermore,
we consider the mass-imbalanced Hubbard model for which the charge Drude weight
decays exponentially with system size, as expected for a non-integrable model.
We analyze the conductivity and diffusion constant as a function of the mass
imbalance and we observe that the conductivity of the lighter component
decreases exponentially fast with the mass-imbalance ratio. While in the
extreme limit of immobile heavy particles, the Falicov-Kimball model, there is
an effective Anderson-localization mechanism leading to a vanishing
conductivity of the lighter species, we resolve finite conductivities for an
inverse mass ratio of .Comment: 13 pages, 11 figure
Transport in the 3-dimensional Anderson model: an analysis of the dynamics on scales below the localization length
Single-particle transport in disordered potentials is investigated on scales
below the localization length. The dynamics on those scales is concretely
analyzed for the 3-dimensional Anderson model with Gaussian on-site disorder.
This analysis particularly includes the dependence of characteristic transport
quantities on the amount of disorder and the energy interval, e.g., the mean
free path which separates ballistic and diffusive transport regimes. For these
regimes mean velocities, respectively diffusion constants are quantitatively
given. By the use of the Boltzmann equation in the limit of weak disorder we
reveal the known energy-dependencies of transport quantities. By an application
of the time-convolutionless (TCL) projection operator technique in the limit of
strong disorder we find evidence for much less pronounced energy dependencies.
All our results are partially confirmed by the numerically exact solution of
the time-dependent Schroedinger equation or by approximative numerical
integrators. A comparison with other findings in the literature is additionally
provided.Comment: 23 pages, 10 figure
Eigenstate Thermalization Hypothesis and Quantum Jarzynski Relation for Pure Initial States
Since the first suggestion of the Jarzynski equality many derivations of this
equality have been presented in both, the classical and the quantum context.
While the approaches and settings greatly differ from one to another, they all
appear to rely on the initial state being a thermal Gibbs state. Here, we
present an investigation of work distributions in driven isolated quantum
systems, starting off from pure states that are close to energy eigenstates of
the initial Hamiltonian. We find that, for the nonintegrable system in quest,
the Jarzynski equality is fulfilled to good accuracy.Comment: 9 pages, 7 figure
Real-time broadening of non-equilibrium density profiles and the role of the specific initial-state realization
The real-time broadening of density profiles starting from non-equilibrium
states is at the center of transport in condensed-matter systems and dynamics
in ultracold atomic gases. Initial profiles close to equilibrium are expected
to evolve according to linear response, e.g., as given by the current
correlator evaluated exactly at equilibrium. Significantly off equilibrium,
linear response is expected to break down and even a description in terms of
canonical ensembles is questionable. We unveil that single pure states with
density profiles of maximum amplitude yield a broadening in perfect agreement
with linear response, if the structure of these states involves randomness in
terms of decoherent off-diagonal density-matrix elements. While these states
allow for spin diffusion in the XXZ spin-1/2 chain at large exchange
anisotropies, coherences yield entirely different behavior.Comment: 7 pages, 7 figures, accepted for publication in Phys. Rev.
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