Fourier-transform spectroscopy of Sr2 and revised ground state potential

Precise potentials for the ground state X1Sigma+g and the minimum region of the excited state 2_1Sigma+u of Sr2 are derived by high resolution Fourier-transform spectroscopy of fluorescence progressions from single frequency laser excitation of Sr2 produced in a heat pipe at 950 Celsius. A change of the rotational assignment by four units compared to an earlier work (G. Gerber, R. M\"oller, and H. Schneider, J. Chem. Phys. 81, 1538 (1984)) is needed for a consistent description leading to a significant shift of the potentials towards longer inter atomic distances. The huge amount of ground state data derived for the three different isotopomers 88Sr2, 86Sr88Sr and 87Sr88Sr (almost 60% of all excisting bound rovibrational ground state levels for the isotopomer 88Sr2) fixes this assignment undoubtedly. The presented ground state potential is derived from the observed transitions for the radial region from 4 to 11 A (9 cm-1 below the asymptote) and is extended to the longe range region by the use of theoretical dispersion coefficients together with already available photoassociation data. New estimations of the scattering lengths for the complete set of isotopic combinations are derived by mass scaling with the derived potential. The data set for the excited state 2_1Sigma+u was sufficient to derive a potential energy curve around the minimum.Comment: 10 pages, 7 figures, some small corrections done especially to the potential description of the excited state (already included in the published journal version

Investigation to develop a process for production of oxide fibers by melt draw technique Final report

Process for production of oxide fibers by melt draw techniqu

Reducing the numerical effort of finite-temperature density matrix renormalization group transport calculations

Finite-temperature transport properties of one-dimensional systems can be studied using the time dependent density matrix renormalization group via the introduction of auxiliary degrees of freedom which purify the thermal statistical operator. We demonstrate how the numerical effort of such calculations is reduced when the physical time evolution is augmented by an additional time evolution within the auxiliary Hilbert space. Specifically, we explore a variety of integrable and non-integrable, gapless and gapped models at temperatures ranging from T=infty down to T/bandwidth=0.05 and study both (i) linear response where (heat and charge) transport coefficients are determined by the current-current correlation function and (ii) non-equilibrium driven by arbitrary large temperature gradients. The modified DMRG algorithm removes an 'artificial' build-up of entanglement between the auxiliary and physical degrees of freedom. Thus, longer time scales can be reached

Elliptic Genera of Symmetric Products and Second Quantized Strings

In this note we prove an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the N-fold symmetric product $M^N/S_N$ of a manifold M to the partition function of a second quantized string theory on the space $M \times S^1$. The generating function of these elliptic genera is shown to be (almost) an automorphic form for O(3,2,Z). In the context of D-brane dynamics, this result gives a precise computation of the free energy of a gas of D-strings inside a higher-dimensional brane.Comment: 17 pages, latex, 1 figure, to appear in Commun. Math. Phy

Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains

We propose an easily implemented approach to study time-dependent correlation functions of one dimensional systems at finite temperature T using the density matrix renormalization group. The entanglement growth inherent to any time-dependent calculation is significantly reduced if the auxiliary degrees of freedom which purify the statistical operator are time evolved with the physical Hamiltonian but reversed time. We exploit this to investigate the long time behavior of current correlation functions of the XXZ spin-1/2 Heisenberg chain. This allows a direct extraction of the Drude weight D at intermediate to large T. We find that D is nonzero -- and thus transport is dissipationless -- everywhere in the gapless phase. At low temperatures we establish an upper bound to D by comparing with bosonization

Unbounded growth of entanglement in models of many-body localization

An important and incompletely answered question is whether a closed quantum system of many interacting particles can be localized by disorder. The time evolution of simple (unentangled) initial states is studied numerically for a system of interacting spinless fermions in one dimension described by the random-field XXZ Hamiltonian. Interactions induce a dramatic change in the propagation of entanglement and a smaller change in the propagation of particles. For even weak interactions, when the system is thought to be in a many-body localized phase, entanglement shows neither localized nor diffusive behavior but grows without limit in an infinite system: interactions act as a singular perturbation on the localized state with no interactions. The significance for proposed atomic experiments is that local measurements will show a large but nonthermal entropy in the many-body localized state. This entropy develops slowly (approximately logarithmically) over a diverging time scale as in glassy systems.Comment: 4 pages, 2 figures, v2. added more dat

Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains

Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient $\pm 0.25$. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on replica or R\'enyi index resulting from flows to different boundary conditions at the entanglement cut.Comment: 4 pages and 4 page appendix, 4 figure