257 research outputs found
Decay of currents for strong interactions
The decay of current autocorrelation functions is investigated for quantum
systems featuring strong 'interactions'. Here, the term interaction refers to
that part of the Hamiltonian causing the (major) decay of the current. On the
time scale before the (first) zero-crossing of the current, its relaxation is
shown to be well described by a suitable perturbation theory in the lowest
orders of the interaction strength, even and especially if interactions are
strong. In this description the relaxation is found to be rather close to a
Gaussian decay and the resulting diffusion coefficient approximately scales
with the inverse interaction strength. These findings are also confirmed by
numerical results from exact diagonalization for several one-dimensional
transport models including spin transport in the Heisenberg chain w.r.t.
different spin quantum numbers, anisotropy, next-to-nearest-neighbor
interaction, or alternating magnetic field; energy transport in the Ising chain
with tilted magnetic field; and transport of excitations in a randomly coupled
modular quantum system. The impact of these results for weak interactions is
finally discussed.Comment: 13 pages, 10 figure
Relation between far-from-equilibrium dynamics and equilibrium correlation functions for binary operators
Linear response theory (LRT) is one of the main approaches to the dynamics of
quantum many-body systems. However, this approach has limitations and requires,
e.g., that the initial state is (i) mixed and (ii) close to equilibrium. In
this paper, we discuss these limitations and study the nonequilibrium dynamics
for a certain class of properly prepared initial states. Specifically, we
consider thermal states of the quantum system in the presence of an additional
static force which, however, become nonequilibrium states when this static
force is eventually removed. While for weak forces the relaxation dynamics is
well captured by LRT, much less is known in the case of strong forces, i.e.,
initial states far away from equilibrium. Summarizing our main results, we
unveil that, for high temperatures, the nonequilibrium dynamics of so-called
binary operators is always generated by an equilibrium correlation function. In
particular, this statement holds true for states in the far-from-equilibrium
limit, i.e., outside the linear response regime. In addition, we confirm our
analytical results by numerically studying the dynamics of local fermionic
occupation numbers and local energy densities in the spin-1/2 Heisenberg chain.
Remarkably, these simulations also provide evidence that our results
qualitatively apply in a more general setting, e.g., in the anisotropic XXZ
model where the local energy is a non-binary operator, as well as for a wider
range of temperature. Furthermore, exploiting the concept of quantum
typicality, all of our findings are not restricted to mixed states, but are
valid for pure initial states as well.Comment: 9 pages, 7 figures. Title changed during peer revie
Energy dynamics in the Heisenberg-Kitaev chain
We study the Heisenberg-Kitaev chain in order to uncover the interplay
between two qualitatively different integrable points in the physics of heat
transport in one dimension. Focusing on high temperatures and using analytical
as well as numerical approaches within linear response theory, we explore
several directions in parameter space including exchange-coupling ratios,
anisotropies, and external magnetic fields. We show the emergence of purely
ballistic energy transport at all integrable points, manifest in pronounced
Drude weights and low-frequency suppression of regular-conductivity
contributions. Moreover, off integrability, we find extended quantum chaotic
regions with vanishing Drude weights and well-defined DC conductivities. In the
vicinity of the Kitaev point, we observe clear signatures of the topological
gap in the response function. This gap coexists with a nonzero Drude weight in
the Kitaev chain.Comment: 7 pages, 8 figures, accepted for publication in Phys. Rev.
Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
We study quantum quenches in the transverse-field Ising model defined on
different lattice geometries such as chains, two- and three-leg ladders, and
two-dimensional square lattices. Starting from fully polarized initial states,
we consider the dynamics of the transverse and the longitudinal magnetization
for quenches to weak, strong, and critical values of the transverse field. To
this end, we rely on an efficient combination of numerical linked cluster
expansions (NLCEs) and a forward propagation of pure states in real time. As a
main result, we demonstrate that NLCEs comprising solely rectangular clusters
provide a promising approach to study the real-time dynamics of two-dimensional
quantum many-body systems directly in the thermodynamic limit. By comparing to
existing data from the literature, we unveil that NLCEs yield converged results
on time scales which are competitive to other state-of-the-art numerical
methods.Comment: Submission to SciPost. 20 pages, 10 figures (+7 pages of references
Burnett coefficients in quantum many-body systems
The Burnett coefficient B is investigated for transport in one-dimensional
quantum many-body systems. Extensive numerical computations in spin-1/2 chains
suggest a linear growth with time, B(t) \sim t, for non-integrable chains
exhibiting diffusive transport. For integrable spin chains in the metallic
regime, on the other hand, we find a cubic growth with time, B(t) \sim -D_m^2
t^3, with the proportionality constant being simply a square of the Drude
weight D_m. The results are corroborated with additional studies in
non-interacting quantum chains and in the classical limit of large-spin chains.Comment: 5 pages, 4 figure
Impact of eigenstate thermalization on the route to equilibrium
The eigenstate thermalization hypothesis (ETH) and the theory of linear
response (LRT) are celebrated cornerstones of our understanding of the physics
of many-body quantum systems out of equilibrium. While the ETH provides a
generic mechanism of thermalization for states arbitrarily far from
equilibrium, LRT extends the successful concepts of statistical mechanics to
situations close to equilibrium. In our work, we connect these cornerstones to
shed light on the route to equilibrium for a class of properly prepared states.
We unveil that, if the off-diagonal part of the ETH applies, then the
relaxation process can become independent of whether or not a state is close to
equilibrium. Moreover, in this case, the dynamics is generated by a single
correlation function, i.e., the relaxation function in the context of LRT. Our
analytical arguments are illustrated by numerical results for idealized models
of random-matrix type and more realistic models of interacting spins on a
lattice. Remarkably, our arguments also apply to integrable quantum systems
where the diagonal part of the ETH may break down.Comment: 5 pages, 4 figures (+ 6 pages, 2 figure
Relevance of the eigenstate thermalization hypothesis for thermal relaxation
We study the validity of the eigenstate thermalization hypothesis (ETH) and
its role for the occurrence of initial-state independent (ISI) equilibration in
closed quantum many-body systems. Using the concept of dynamical typicality, we
present an extensive numerical analysis of energy exchange in integrable and
nonintegrable spin-1/2 systems of large size outside the range of exact
diagonalization. In case of nonintegrable systems, our finite-size scaling
shows that the ETH becomes valid in the thermodynamic limit and can serve as
the underlying mechanism for ISI equilibration. In case of integrable systems,
however, indication of ISI equilibration has been observed despite the
violation of the ETH. We establish a connection between this observation and
the need of choosing a proper parameter within the ETH.Comment: 6 pages, 5 figure
Comment on: "Fluctuation Theorem for Many-Body Pure Quantum States" and Reply to "arXiv:1712.05172"
We comment on: E. Iyoda, K. Kaneko, and T. Sagawa, "Fluctuation Theorem for
Many-Body Pure Quantum States", Phys. Rev. Lett. 119, 100601 (2017). We also
respond to the reply by the afore mentioned authors: "arXiv:1712.05172". The
response at hand concludes our discussion of the subject on the arXiv.Comment: 5 pages, 3 figure
Spin-current autocorrelations from single pure-state propagation
We demonstrate that the concept of quantum typicality allows for significant
progress in the study of real-time spin dynamics and transport in quantum
magnets. To this end, we present a numerical analysis of the spin-current
autocorrelation function of the antiferromagnetic and anisotropic spin-1/2
Heisenberg chain as inferred from propagating only a single pure state,
randomly chosen as a "typical" representative of the statistical ensemble.
Comparing with existing time-dependent density-matrix renormalization group
(tDMRG) data, we show that typicality is fulfilled extremely well, consistent
with an error of our approach, which is perfectly under control and vanishes in
the thermodynamic limit. In the long-time limit, our results provide for a new
benchmark for the enigmatic spin Drude weight, which we obtain from chains as
long as L=33 sites, i.e., from Hilbert spaces of dimensions almost O(10^4)
larger than in existing exact-diagonalization studies.Comment: 5 pages, 4 figures, accepted for publication in Physical Review
Letter
Spin and energy currents in integrable and nonintegrable spin-1/2 chains: A typicality approach to real-time autocorrelations
We use the concept of typicality to study the real-time dynamics of spin and
energy currents in spin-1/2 models in one dimension and at nonzero
temperatures. These chains are the integrable XXZ chain and a nonintegrable
modification due to the presence of a staggered magnetic field oriented in z
direction. In the framework of linear response theory, we numerically calculate
autocorrelation functions by propagating a single pure state, drawn at random
as a typical representative of the full statistical ensemble. By comparing to
small-system data from exact diagonalization (ED) and existing short-time data
from time-dependent density matrix renormalization group (tDMRG), we show that
typicality is satisfied in finite systems over a wide range of temperature and
is fulfilled in both, integrable and nonintegrable systems. For the integrable
case, we calculate the long-time dynamics of the spin current and extract the
spin Drude weight for large systems outside the range of ED. We particularly
provide strong evidence that the high-temperature Drude weight vanishes at the
isotropic point. For the nonintegrable case, we obtain the full relaxation
curve of the energy current and determine the heat conductivity as a function
of magnetic field, exchange anisotropy, and temperature.Comment: 14 pages, 14 figures, accepted for publication in Phys. Rev.
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