74 research outputs found
Thermal transport of the XXZ chain in a magnetic field
We study the heat conduction of the spin-1/2 XXZ chain in finite magnetic
fields where magnetothermal effects arise. Due to the integrability of this
model, all transport coefficients diverge, signaled by finite Drude weights.
Using exact diagonalization and mean-field theory, we analyze the temperature
and field dependence of the thermal Drude weight for various exchange
anisotropies under the condition of zero magnetization-current flow. First, we
find a strong magnetic field dependence of the Drude weight, including a
suppression of its magnitude with increasing field strength and a non-monotonic
field-dependence of the peak position. Second, for small exchange anisotropies
and magnetic fields in the massless as well as in the fully polarized regime
the mean-field approach is in excellent agreement with the exact
diagonalization data. Third, at the field-induced quantum critical line between
the para- and ferromagnetic region we propose a universal low-temperature
behavior of the thermal Drude weight.Comment: 9 pages REVTeX4 including 5 figures, revised version, refs. added,
typos correcte
Non-dissipative Thermal Transport and Magnetothermal Effect for the Spin-1/2 Heisenberg Chain
Anomalous magnetothermal effects are discussed in the spin-1/2 Heisenberg
chain. The energy current is related to one of the non-trivial conserved
quantities underlying integrability and therefore both the diagonal and off
diagonal dynamical correlations of spin and energy current diverge. The
energy-energy and spin-energy current correlations at finite temperatures are
exactly calculated by a lattice path integral formulation. The low-temperature
behavior of the thermomagnetic (magnetic Seebeck) coefficient is also
discussed. Due to effects of strong correlations, we observe the magnetic
Seebeck coefficient changes sign at certain interaction strengths and magnetic
fields.Comment: 4 pages, references added, typos corrected, Conference proceedings of
SPQS 2004, Sendai, Japa
Magnon Heat Transport in doped
We present results of the thermal conductivity of and single-crystals which represent model systems for the
two-dimensional spin-1/2 Heisenberg antiferromagnet on a square lattice. We
find large anisotropies of the thermal conductivity, which are explained in
terms of two-dimensional heat conduction by magnons within the CuO planes.
Non-magnetic Zn substituted for Cu gradually suppresses this magnon thermal
conductivity . A semiclassical analysis of
is shown to yield a magnon mean free path which scales
linearly with the reciprocal concentration of Zn-ions.Comment: 4 pages, 3 figure
Thermomagnetic Power and Figure of Merit for Spin-1/2 Heisenberg Chain
Transport properties in the presence of magnetic fields are numerically
studied for the spin-1/2 Heisenberg XXZ chain. The breakdown of the
spin-reversal symmetry due to the magnetic field induces the magnetothermal
effect. In analogy with the thermoelectric effect in electron systems, the
thermomagnetic power (magnetic Seebeck coefficient) is provided, and is
numerically evaluated by the exact diagonalization for wide ranges of
temperatures and various magnetic fields. For the antiferromagnetic regime, we
find the magnetic Seebeck coefficient changes sign at certain temperatures,
which is interpreted as an effect of strong correlations. We also compute the
thermomagnetic figure of merit determining the efficiency of the thermomagnetic
devices for cooling or power generation.Comment: 8 page
Transport through quantum dots: A combined DMRG and cluster-embedding study
The numerical analysis of strongly interacting nanostructures requires
powerful techniques. Recently developed methods, such as the time-dependent
density matrix renormalization group (tDMRG) approach or the embedded-cluster
approximation (ECA), rely on the numerical solution of clusters of finite size.
For the interpretation of numerical results, it is therefore crucial to
understand finite-size effects in detail. In this work, we present a careful
finite-size analysis for the examples of one quantum dot, as well as three
serially connected quantum dots. Depending on odd-even effects, physically
quite different results may emerge from clusters that do not differ much in
their size. We provide a solution to a recent controversy over results obtained
with ECA for three quantum dots. In particular, using the optimum clusters
discussed in this paper, the parameter range in which ECA can reliably be
applied is increased, as we show for the case of three quantum dots. As a
practical procedure, we propose that a comparison of results for static
quantities against those of quasi-exact methods, such as the ground-state
density matrix renormalization group (DMRG) method or exact diagonalization,
serves to identify the optimum cluster type. In the examples studied here, we
find that to observe signatures of the Kondo effect in finite systems, the best
clusters involving dots and leads must have a total z-component of the spin
equal to zero.Comment: 16 pages, 14 figures, revised version to appear in Eur. Phys. J. B,
additional reference
Bond-impurity induced bound states in disordered spin-1/2 ladders
We discuss the effect of weak bond-disorder in two-leg spin ladders on the
dispersion relation of the elementary triplet excitations with a particular
focus on the appearance of bound states in the spin gap. Both the cases of
modified exchange couplings on the rungs and the legs of the ladder are
analyzed. Based on a projection on the single-triplet subspace, the
single-impurity and small cluster problems are treated analytically in the
strong-coupling limit. Numerically, we study the problem of a single impurity
in a spin ladder by exact diagonalization to obtain the low-lying excitations.
At finite concentrations and to leading order in the inter-rung coupling, we
compare the spectra obtained from numerical diagonalization of large systems
within the single-triplet subspace with the results of diagrammatic techniques,
namely low-concentration and coherent-potential approximations. The
contribution of small impurity clusters to the density of states is also
discussed.Comment: 9 pages REVTeX4 including 7 figures, final version; Fig. 5 modifie
Local Policy Search in a Convex Space and Conservative Policy Iteration as Boosted Policy Search
International audienceLocal Policy Search is a popular reinforcement learning approach for handling large state spaces. Formally, it searches locally in a parameterized policy space in order to maximize the associated value function averaged over some pre-defined distribution. The best one can hope in general from such an approach is to get a local optimum of this criterion. The first contribution of this article is the following surprising result: if the policy space is convex, any (approximate) local optimum enjoys a global performance guarantee. Unfortunately, the convexity assumption is strong: it is not satisfied by commonly used parameterizations and designing a parameterization that induces this property seems hard. A natural so-lution to alleviate this issue consists in deriving an algorithm that solves the local policy search problem using a boosting approach (constrained to the convex hull of the policy space). The resulting algorithm turns out to be a slight generalization of conservative policy iteration; thus, our second contribution is to highlight an original connection between local policy search and approximate dynamic pro-gramming
A Novel Approach to Study Highly Correlated Nanostructures: The Logarithmic Discretization Embedded Cluster Approximation
This work proposes a new approach to study transport properties of highly
correlated local structures. The method, dubbed the Logarithmic Discretization
Embedded Cluster Approximation (LDECA), consists of diagonalizing a finite
cluster containing the many-body terms of the Hamiltonian and embedding it into
the rest of the system, combined with Wilson's idea of a logarithmic
discretization of the representation of the Hamiltonian. The physics associated
with both one embedded dot and a double-dot side-coupled to leads is discussed
in detail. In the former case, the results perfectly agree with Bethe ansatz
data, while in the latter, the physics obtained is framed in the conceptual
background of a two-stage Kondo problem. A many-body formalism provides a solid
theoretical foundation to the method. We argue that LDECA is well suited to
study complicated problems such as transport through molecules or quantum dot
structures with complex ground states.Comment: 17 pages, 13 figure
Thermodyamic bounds on Drude weights in terms of almost-conserved quantities
We consider one-dimensional translationally invariant quantum spin (or
fermionic) lattices and prove a Mazur-type inequality bounding the
time-averaged thermodynamic limit of a finite-temperature expectation of a
spatio-temporal autocorrelation function of a local observable in terms of
quasi-local conservation laws with open boundary conditions. Namely, the
commutator between the Hamiltonian and the conservation law of a finite chain
may result in boundary terms only. No reference to techniques used in Suzuki's
proof of Mazur bound is made (which strictly applies only to finite-size
systems with exact conservation laws), but Lieb-Robinson bounds and exponential
clustering theorems of quasi-local C^* quantum spin algebras are invoked
instead. Our result has an important application in the transport theory of
quantum spin chains, in particular it provides rigorous non-trivial examples of
positive finite-temperature spin Drude weight in the anisotropic Heisenberg XXZ
spin 1/2 chain [Phys. Rev. Lett. 106, 217206 (2011)].Comment: version as accepted by Communications in Mathematical Physics (22
pages with 2 pdf-figures
Thermal conductivity of anisotropic and frustrated spin-1/2 chains
We analyze the thermal conductivity of anisotropic and frustrated spin-1/2
chains using analytical and numerical techniques. This includes mean-field
theory based on the Jordan-Wigner transformation, bosonization, and exact
diagonalization of systems with N<=18 sites. We present results for the
temperature dependence of the zero-frequency weight of the conductivity for
several values of the anisotropy \Delta. In the gapless regime, we show that
the mean-field theory compares well to known results and that the
low-temperature limit is correctly described by bosonization. In the
antiferromagnetic and ferromagnetic gapped regime, we analyze the temperature
dependence of the thermal conductivity numerically. The convergence of the
finite-size data is remarkably good in the ferromagnetic case. Finally, we
apply our numerical method and mean-field theory to the frustrated chain where
we find a good agreement of these two approaches on finite systems. Our
numerical data do not yield evidence for a diverging thermal conductivity in
the thermodynamic limit in case of the antiferromagnetic gapped regime of the
frustrated chain.Comment: 4 pages REVTeX4 including 6 figures; published version, main
modification: added emphasis that the data of our Fig. 3 point to a vanishing
of the thermal Drude weight in the thermodynamic limit in this cas
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