| Abstract |
The field of low dimensional quantum systems remains active for decades for both
theoretical and experimental research. This work is a contribution to the theoretical
study of one-dimensional quantum magnets. In parallel with our theoretical study,
several experimental teams all around the globe work to fabricate novel materials which
are highly anisotropic and can be considered as good realizations of one-dimensional
systems. Moreover, the unconventional transport properties of these systems makes
them very promising candidates for technological applications.
We focus on the transport properties of one-dimensional quantum magnets described
by the celebrated anisotropic Heisenberg Hamiltonian. In the pure spin- 1/2 Heisenberg model, which is an integrable model, heat transport is really unique since
the energy current is a constant of motion leading to ballistic heat transport. Thus,
the interplay of integrability and defects is theoretically challenging and we attempt to
shed light on various aspects of this issue employing primarily numerical diagonalization
techniques.
First, we discuss the effect of static disorder accounting for the onset of Anderson
localization. In a many body system interactions can delocalize the localized states
leading the system to a diffusive state. The main conclusion is that the dc transport
of the many body system is finite for any finite temperature. On the contrary, at zero
temperature for the interacting system or at any temperature for the non-interacting
one, spin and thermal dc conductivities vanish in the strong disorder regime.
Second, we consider the more subtle effect of a single non-magnetic impurity and
whether this perturbation is capable to break the integrability of the system. We use
as criteria for the breaking of integrability the level statistics of the system and the spin
stiffness in the easy plane regime. Moreover, for a single impurity case it turns out that
the thermal conductivity is a unique probe since the only scattering mechanism for the
thermal transport comes from the impurity. We show that a single impurity in a many
body system renders ballistic transport incoherent at high energies in contrast with the
non-interacting case where the impurity only renormalizes the charge stiffness.
Third, is the effect of a single magnetic impurity of spin S disturbing the spin- 1
2
Heisenberg chain. We consider the impurity to be located either out of the chain or
to be embedded to it. In the former case, we find a universal scaling with both the
lattice size, and the perturbation strength. On the other hand, the embedded impurity
in the chain is a severe perturbation and dominates easily the behavior of the transport
quantities. Useful conclusions can be obtained by analytical arguments in the strong
host-impurity coupling limit.
Last, as far as the temperature dependence is concerned for the single impurity
cases, we seek cutting-healing phenomena. More particularly, for decreasing temperature
we find that the chain is (cut)healed for (anti)ferromagnetic easy axis anisotropy
for all types of single impurities|single weak link, local field, magnetic impurity out
of the chain, magnetic impurity embedded in the chain. In the same concept is the
(cutting)healing of the isotropic Heisenberg chain with decreasing temperature in the
presence of (a single)two consecutive weak links.
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Conductivities of magnetic chains with (non-)magnetic impurities
