Quantum Phases of the Shastry-Sutherland Kondo Lattice: Implications for the Global Phase Diagram of Heavy Fermion Metals

Considerable recent theoretical and experimental efforts have been devoted to the study of quantum criticality and novel phases of antiferromagnetic heavy-fermion metals. In particular, quantum phase transitions have been discovered in the compound Yb$_2$Pt$_2$Pb. These developments have motivated us to study the competition between the RKKY and Kondo interactions on the Shastry-Sutherland lattice. We determine the zero-temperature phase diagram as a function of magnetic frustration and Kondo coupling within a slave-fermion approach. Pertinent phases include the Shastry-Sutherland valence bond solid and heavy Fermi liquid. In the presence of antiferromagnetic order, our zero-temperature phase diagram is remarkably similar to the global phase diagram proposed earlier based on general grounds. We discuss the implications of our results for the experiments on Yb$_2$Pt$_2$Pb and other geometrically frustrated heavy fermion compounds.Comment: 5 pages 4 figures - Supplementary Material 4 pages 6 figures. Updated with published versio

Effective potential for composite operators and for an auxiliary scalar field in a Nambu-Jona-Lasinio model

We derive the effective potentials for composite operators in a Nambu-Jona-Lasinio (NJL) model at zero and finite temperature and show that in each case they are equivalent to the corresponding effective potentials based on an auxiliary scalar field. The both effective potentials could lead to the same possible spontaneous breaking and restoration of symmetries including chiral symmetry if the momentum cutoff in the loop integrals is large enough, and can be transformed to each other when the Schwinger-Dyson (SD) equation of the dynamical fermion mass from the fermion-antifermion vacuum (or thermal) condensates is used. The results also generally indicate that two effective potentials with the same single order parameter but rather different mathematical expressions can still be considered physically equivalent if the SD equation corresponding to the extreme value conditions of the two potentials have the same form.Comment: 7 pages, no figur

T-Shape Molecular Heat Pump

We report on the first molecular device of heat pump modeled by a T-shape Frenkel-Kontorova lattice. The system is a three-terminal device with the important feature that the heat can be pumped from the low-temperature region to the high-temperature region through the third terminal. The pumping action is achieved by applying a stochastic external force that periodically modulates the atomic temperature. The temperature, the frequency and the system size dependence of heat pump are briefly discussed.Comment: 6 figure

Torsion in Graph Homology

Khovanov homology for knots has generated a flurry of activity in the topology community. This paper studies the Khovanov type cohomology for graphs with a special attention to torsions. When the underlying algebra is $\mathbb{Z}[x]/(x^2)$, we determine precisely those graphs whose cohomology contains torsion. For a larger class of algebras, we show that torsion often occurs. Our investigation of torsion led to other related general results. The ideas of this paper could potentially be used to predict the Khovanov-Rozansky $sl(m)$ homology of knots (in particular $(2,n)$ torus knots). We also predict that our work is connected with Hochschild and Connes cyclic homology of algebras.Comment: 45 pages, 20 figures, Fundamenta Mathematicae, 190, 2006, to appea

Determination of f+K(0)f_+^K(0) and Extraction of ∣Vcs∣|V_{cs}| from Semileptonic DD Decays

By globally analyzing all existing measured branching fractions and partial rates in different four momentum transfer-squared $q^2$ bins of $D\to Ke^+\nu_e$ decays, we obtain the product of the form factor and magnitude of CKM matrix element $V_{cs}$ to be $f_+^K(0)|V_{cs}|=0.717\pm0.004$. With this product, we determine the $D\to K$ semileptonic form factor $f_+^K(0)=0.737\pm0.004\pm0.000$ in conjunction with the value of $|V_{cs}|$ determined from the SM global fit. Alternately, with the product together with the input of the form factor $f_+^K(0)$ calculated in lattice QCD recently, we extract $|V_{cs}|^{D\to Ke^+\nu_e}=0.962\pm0.005\pm0.014$, where the error is still dominated by the uncertainty of the form factor calculated in lattice QCD. Combining the $|V_{cs}|^{D_s^+\to\ell^+\nu_\ell}=1.012\pm0.015\pm0.009$ extracted from all existing measurements of $D^+_s\to\ell^+\nu_\ell$ decays and $|V_{cs}|^{D\to Ke^+\nu_e}=0.962\pm0.005\pm0.014$ together, we find the most precisely determined $|V_{cs}|$ to be $|V_{cs}|=0.983\pm0.011$, which improves the accuracy of the PDG'2014 value $|V_{cs}|^{\rm PDG'2014}=0.986\pm0.016$ by $45\%$

Replica study of pinned bubble crystals

In higher Landau levels ($N>1$), the ground state of the two-dimensional electron gas in a strong perpendicular magnetic field evolves from a Wigner crystal for small filling $\nu$ of the partially filled Landau level, into a succession of bubble states with increasing number of guiding centers per bubble as $\nu$ increases, to a modulated stripe state near $\nu =0.5$. In this work, we compute the frequency-dependent longitudinal conductivity $\sigma_{xx}(\omega)$ of the Wigner and bubble crystal states in the presence of disorder. We apply an elastic theory to the crystal states which is characterized by a shear and a bulk modulus. We obtain both moduli from the microscopic time-dependent Hartree-Fock approximation. We then use the replica and Gaussian variational methods to handle the effects of disorder. Within the semiclassical approximation we get the dynamical conductivity as well as the pinning frequency as functions of the Landau level filling factor and compare our results with recent microwave experiments.Comment: 19 pages and 6 eps figure

THE STRUCTURE OF HUMAN ACHILLES TENDON AND ITS BIOMECHANICAL SIGNIFICANCE

The morphological characteristics, particularly the rotation structure, of human Achilles tendon were investigated on 21 I lower limb specimens 101 Achilles tendons of male adult specimens were measured The structure, function and biomechanical properties of the tendon, as well as inter-individual differences in tendon rotation and morphological indicators of tendon injury have been discussed The tendon fibers of two muscle groups (gastrocnemius and soleus) intersect each other in a rotating manner. This rotation is from medial to lateral The rotation starts at 12-15 cm above the calcaneum but becomes most obvious at approximately 5 cm above h e calcaneum. The degrees of rotation vary in every body and were divided into 3 types: light, medium and heavy. The percentage of h e 3 types of rotation are 58.29f 3.39, 3270f 3.23,9.01f 1.86, respectively. No significant deferences were found between two distinct sexes, sides, age-groups or races. The tendon length, upper-width,lower-widthand lower-thickness of adult Chinese males are 19.77f 0.246.58f 0.18, I.5Of Q04,0.68f 0.01 cm, respectively. The tendon rotation structure has some biomechanical implications for he tendon's adaptation lo the tremendous tractive forces developed during special situations Along with common factors known to result in tendon injury, we believe structural weakness to be one of the most important factors resulting in tendon injury. Common weaknesses in morphological structure are: the most avascular part of the tendon (approx. 44 cm above insertion), which is the most obvious position of rotation; the presence of a large number of Type 111 collagen in the tendon; he light rotation pattern of this tendon among the great majority of human beings; and the damage caused by Le saw-like action between h e two parts of tendon fibers In addition, owing to the two-joint (knee and ankle) spanning of the gastrocnemius, a stretched tendon will develop even greater tension and easily tear when the quadriceps muscle group contracts strongly during knee extension