Generalised Shastry-Sutherland Models in three and higher dimensions

We construct Heisenberg anti-ferromagnetic models in arbitrary dimensions that have isotropic valence bond crystals (VBC) as their exact ground states. The d=2 model is the Shastry-Sutherland model. In the 3-d case we show that it is possible to have a lattice structure, analogous to that of SrCu_2(BO_3)_2, where the stronger bonds are associated with shorter bond lengths. A dimer mean field theory becomes exact at d -> infinity and a systematic 1/d expansion can be developed about it. We study the Neel-VBC transition at large d and find that the transition is first order in even but second order in odd dimensions.Comment: Published version; slightly expande

Geodesics for Efficient Creation and Propagation of Order along Ising Spin Chains

Experiments in coherent nuclear and electron magnetic resonance, and optical spectroscopy correspond to control of quantum mechanical ensembles, guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and decoherence and to optimize the sensitivity of the experiments. Here we give efficient syntheses of various unitary transformations on Ising spin chains of arbitrary length. The efficient realization of the unitary transformations presented here is obtained by computing geodesics on a sphere under a special metric. We show that contrary to the conventional belief, it is possible to propagate a spin order along an Ising spin chain with coupling strength J (in units of Hz), significantly faster than 1/(2J) per step. The methods presented here are expected to be useful for immediate and future applications involving control of spin dynamics in coherent spectroscopy and quantum information processing

Effect of Randomness on Quantum Data Buses of Heisenberg Spin Chains

A strongly coupled spin chain can mediate long-distance effective couplings or entanglement between remote qubits, and can be used as a quantum data bus. We study how the fidelity of a spin-1/2 Heisenberg chain as a spin bus is affected by static random exchange couplings and magnetic fields. We find that, while non-uniform exchange couplings preserve the isotropy of the qubit effective couplings, they cause the energy levels, the eigenstates, and the magnitude of the couplings to vary locally. On the other hand, random local magnetic fields lead to an avoided level crossing for the bus ground state manifold, and cause the effective qubit couplings to be anisotropic. Interestingly, the total magnetic moment of the ground state of an odd-size bus may not be parallel to the average magnetic field. Its alignment depends on both the direction of the average field and the field distribution, in contrast with the ground state of a single spin which always aligns with the applied magnetic field to minimize the Zeeman energy. Lastly, we calculate sensitivities of the spin bus to such local variations, which are potentially useful for evaluating decoherence when dynamical fluctuations in the exchange coupling or magnetic field are considered

Multiple-spin coherence transfer in linear Ising spin chains and beyond: numerically-optimized pulses and experiments

We study multiple-spin coherence transfers in linear Ising spin chains with nearest neighbor couplings. These constitute a model for efficient information transfers in future quantum computing devices and for many multi-dimensional experiments for the assignment of complex spectra in nuclear magnetic resonance spectroscopy. We complement prior analytic techniques for multiple-spin coherence transfers with a systematic numerical study where we obtain strong evidence that a certain analytically-motivated family of restricted controls is sufficient for time-optimality. In the case of a linear three-spin system, additional evidence suggests that prior analytic pulse sequences using this family of restricted controls are time-optimal even for arbitrary local controls. In addition, we compare the pulse sequences for linear Ising spin chains to pulse sequences for more realistic spin systems with additional long-range couplings between non-adjacent spins. We experimentally implement the derived pulse sequences in three and four spin systems and demonstrate that they are applicable in realistic settings under relaxation and experimental imperfections-in particular-by deriving broadband pulse sequences which are robust with respect to frequency offsets.Comment: 11 page

A Holstein-Primakoff and a Dyson realization for the quantum algebra Uq[sl(n+1)]U_q[sl(n+1)]

The known Holstein-Primakoff and Dyson realizations of the Lie algebra $sl(n+1), n=1,2,...$ in terms of Bose operators (Okubo S 1975 J. Math. Phys. 16 528) are generalized to the class of the quantum algebras $U_q[sl(n+1)]$ for any $n$. It is shown how the elements of $U_q[sl(n+1)]$ can be expressed via $n$ pairs of Bose creation and annihilation operators.Comment: 5 pages, Te

Quantum-Mechanical Position Operator and Localization in Extended Systems

We introduce a fundamental complex quantity, $z_{L}$, which allows us to discriminate between a conducting and non-conducting thermodynamic phase in extended quantum systems. Its phase can be related to the expectation value of the position operator, while its modulus provides an appropriate definition of a localization length. The expressions are valid for {\it any} fractional particle filling. As an illustration we use $z_{L}$ to characterize insulator to ``superconducting'' and Mott transitions in one-dimensional lattice models with infinite on-site Coulomb repulsion at quarter filling.Comment: 4 pages, REVTEX, 1 ps figure

Sound localization with bilateral bone conduction devices

Purpose To investigate sound localization in patients bilaterally fitted with bone conduction devices (BCDs). Additionally, clinically applicable methods to improve localization accuracy were explored. Methods Fifteen adults with bilaterally fitted percutaneous BCDs were included. At baseline, sound localization, (un)aided pure-tone thresholds, device use, speech, spatial and qualities of hearing scale (SSQ) and York hearing-related quality of life (YHRQL) questionnaire were measured. Settings to optimize sound localizing were added to the BCDs. At 1 month, sound localization was assessed again and localization was practiced with a series of sounds with visual feedback. At 3 months, localization performance, device use and questionnaire scores were determined again. Results At baseline, one patient with congenital hearing loss demonstrated near excellent localization performance and four other patients (three with congenital hearing loss) localized sounds (quite) accurately. Seven patients with acquired hearing loss were able to lateralize sounds, i.e. identify whether sounds were coming from the left or right side, but could not localize sounds accurately. Three patients (one with congenital hearing loss) could not even lateralize sounds correctly. SSQ scores were significantly higher at 3 months. Localization performance, device use and YHRQL scores were not significantly different between visits. Conclusion In this study, the majority of experienced bilateral BCD users could lateralize sounds and one third was able to localize sounds (quite) accurately. The localization performance was robust and stable over time. Although SSQ scores were increased at the last visit, optimizing device settings and a short practice session did not improve sound localization

A non-Hermitian critical point and the correlation length of strongly correlated quantum systems

We study a non-Hermitian generalization of quantum systems in which an imaginary vector potential is added to the momentum operator. In the tight-binding approximation, we make the hopping energy asymmetric in the Hermitian Hamiltonian. In a previous article, we conjectured that the non-Hermitian critical point where the energy gap vanishes is equal to the inverse correlation length of the Hermitian system and we confirmed the conjecture for two exactly solvable systems. In this article, we present more evidence for the conjecture. We also argue the basis of our conjecture by noting the dispersion relation of the elementary excitation.Comment: 25 pages, 18 figure

Finite Temperature DMRG Investigation of the Spin-Peierls Transition in CuGeO3_3

We present a numerical study of thermodynamical properties of dimerized frustrated Heisenberg chains down to extremely low temperatures with applications to CuGeO$_3$. A variant of the finite temperature density matrix renormalization group (DMRG) allows the study of the dimerized phase previously unaccessible to ab initio calculations. We investigate static dimerized systems as well as the instability of the quantum chain towards lattice dimerization. The crossover from a quadratic response in the free energy to the distortion field at finite temperature to nonanalytic behavior at zero temperature is studied quantitatively. Various physical quantities are derived and compared with experimental data for CuGeO$_3$ such as magnetic dimerization, critical temperature, susceptibility and entropy.Comment: LaTeX, 5 pages, 5 eps figures include

Stochastic conversions of TeV photons into axion-like particles in extragalactic magnetic fields

Very-high energy photons emitted by distant cosmic sources are absorbed on the extragalactic background light (EBL) during their propagation. This effect can be characterized in terms of a photon transfer function at Earth. The presence of extragalactic magnetic fields could also induce conversions between very high-energy photons and hypothetical axion-like particles (ALPs). The turbulent structure of the extragalactic magnetic fields would produce a stochastic behaviour in these conversions, leading to a statistical distribution of the photon transfer functions for the different realizations of the random magnetic fields. To characterize this effect, we derive new equations to calculate the mean and the variance of this distribution. We find that, in presence of ALP conversions, the photon transfer functions on different lines of sight could have relevant deviations with respect to the mean value, producing both an enhancement or a suppression in the observable photon flux with respect to the expectations with only absorption. As a consequence, the most striking signature of the mixing with ALPs would be a reconstructed EBL density from TeV photon observations which appears to vary over different directions of the sky: consistent with standard expectations in some regions, but inconsistent in others.Comment: v2: 22 pages, 5 eps figures. Minor changes. A reference added. Matches the version published on JCA