2,614 research outputs found
Driving XXZ spin chains: Magnetic-field and boundary effects
Using the time-evolving block decimation, we study the spin transport through
spin-1/2 and spin-1 XXZ chains subjected to an external magnetic field and
contacted to noninteracting fermionic leads. For generic system-lead couplings,
the spin conductance exhibits several resonances as a function of the
magnetic-field strength. In the spin-1/2 but not the spin-1 case, the coupling
to the leads can be fine-tuned to reach a conducting fixed point, where the
peak structure is washed out and the spin conductance is large throughout the
gapless Luttinger-liquid phase. For the Haldane phase of the spin-1 chain, we
analyse how the spin transport is affected by spin-1/2 edge states, and argue
that two-impurity Kondo physics is realised.Comment: 7 pages, 8 figures, revised versio
A Canonical Model Construction for Iteration-Free PDL with Intersection
We study the axiomatisability of the iteration-free fragment of Propositional
Dynamic Logic with Intersection and Tests. The combination of program
composition, intersection and tests makes its proof-theory rather difficult. We
develop a normal form for formulae which minimises the interaction between
these operators, as well as a refined canonical model construction. From these
we derive an axiom system and a proof of its strong completeness.Comment: In Proceedings GandALF 2016, arXiv:1609.0364
The Fixpoint-Iteration Algorithm for Parity Games
It is known that the model checking problem for the modal mu-calculus reduces
to the problem of solving a parity game and vice-versa. The latter is realised
by the Walukiewicz formulas which are satisfied by a node in a parity game iff
player 0 wins the game from this node. Thus, they define her winning region,
and any model checking algorithm for the modal mu-calculus, suitably
specialised to the Walukiewicz formulas, yields an algorithm for solving parity
games. In this paper we study the effect of employing the most straight-forward
mu-calculus model checking algorithm: fixpoint iteration. This is also one of
the few algorithms, if not the only one, that were not originally devised for
parity game solving already. While an empirical study quickly shows that this
does not yield an algorithm that works well in practice, it is interesting from
a theoretical point for two reasons: first, it is exponential on virtually all
families of games that were designed as lower bounds for very particular
algorithms suggesting that fixpoint iteration is connected to all those.
Second, fixpoint iteration does not compute positional winning strategies. Note
that the Walukiewicz formulas only define winning regions; some additional work
is needed in order to make this algorithm compute winning strategies. We show
that these are particular exponential-space strategies which we call
eventually-positional, and we show how positional ones can be extracted from
them.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Giant response to weak pumping in quantum systems with approximate symmetries
Our environment and nature as a whole are fundamentally not in equilibrium. The existence of life on earth is only possible for this reason. Everyday examples of non-equilibrium processes are various weather phenomena driven by air and heat flows, traffic jams on motorways or the swarm behavior of animals in groups. These are just a few examples of many more phenomena and motivate a better understanding of non-equilibrium processes in classical as well as quantum systems.
Non-equilibrium means that the known concepts, which are valid in equilibrium, are generally not or only approximately applicable. In equilibrium, all macroscopic currents add on average up to zero and the configuration of a system is solely determined by the fundamental principle of entropy maximization and the symmetries present in the system. According to the Noether theorem, which represents one of the most fundamental relations in physics, each continuous symmetry is associated with a conservation law.
In this thesis, we consider quantum systems that have a set of conservation laws of which some are weakly violated by an external perturbation. We show that under these circumstances highly non-equilibrium states can be reached which are characterized by large currents. The phenomenon that a small perturbation can have a very large effect if it breaks a conservation law can, for example, be illustrated with a greenhouse. Inside the greenhouse the energy is approximately conserved due to the good insulation. As a consequence, the interior can be heated up to very high temperatures by even weak sunlight
Critical behavior of the extended Hubbard model with bond dimerization
Exploiting the matrix-product-state based density-matrix renormalization
group (DMRG) technique we study the one-dimensional extended (-) Hubbard
model with explicit bond dimerization in the half-filled band sector. In
particular we investigate the nature of the quantum phase transition, taking
place with growing ratio between the symmetry-protected-topological and
charge-density-wave insulating states. The (weak-coupling) critical line of
continuous Ising transitions with central charge terminates at a
tricritical point belonging to the universality class of the dilute Ising model
with . We demonstrate that our DMRG data perfectly match with
(tricritical) Ising exponents, e.g., for the order parameter (1/24)
and correlation length (5/9). Beyond the tricritical Ising point, in
the strong-coupling regime, the quantum phase transition becomes first order.Comment: 6 pages, 7 figures, contributions to SCES 201
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