Competition Between Charge-Density Waves and Superconductivity in Striped Systems

Switching on interchain coupling in a system of one-dimensional strongly interacting chains often leads to an ordered state. Quite generally, there is a competition between an insulating charge-density-wave and a superconducting state. In the case of repulsive interactions, charge-density wave usually wins over superconductivity. Here, we show that a suitable modulation in the form of a period 4 bond-centered stripe can reverse this balance even in the repulsive case and produce a superconducting state with relatively high temperature.Comment: Proceedings of SCES 04, 2 page

Smoothing and Rothe's method for Stefan problems in enthalpy form

AbstractThe classical two-phase Stefan problem as well as its weak variational formulation model the connection between the different phases of the considered material by interface conditions at the occurring free boundary or by a jump of the enthalpy. One way to treat the corresponding discontinuous variational problems consists in its embedding into a family of continuous ones and applying some standard techniques to the chosen approximation problems. The aim of the present paper is to analyze a semi-discretization via Rothe's method and its convergence behavior in dependence of the smoothing parameter. While in Grossmann et al. (Optimization, in preparation) the treatment of the Stefan problem is based on the given variable, i.e. the temperature, here first a transformation via the smoothed enthalpy is applied. Numerical experiments indicate a higher stability of the discretization by Rothe's method. In addition, to avoid inner iterations a frozen coefficient approach as common in literature is used

Frustrated three-leg spin tubes: from spin 1/2 with chirality to spin 3/2

Motivated by the recent discovery of the spin tube [(CuCl$_2$tachH)$_3$Cl]Cl$_2$, we investigate the properties of a frustrated three-leg spin tube with antiferromagnetic intra-ring and inter-ring couplings. We pay special attention to the evolution of the properties from weak to strong inter-ring coupling and show on the basis of extensive density matrix renormalization group and exact diagonalization calculations that the system undergoes a first-order phase transition between a dimerized gapped phase at weak coupling that can be described by the usual spin-chirality model and a gapless critical phase at strong coupling that can be described by an effective spin-3/2 model. We also show that there is a magnetization plateau at 1/3 in the gapped phase and slightly beyond. The implications for [(CuCl$_2$tachH)$_3$Cl]Cl$_2$ are discussed, with the conclusion that this system behaves essentially as a spin-3/2 chain.Comment: 8 pages, 9 figures, revised versio

The Density Matrix Renormalization Group applied to single-particle Quantum Mechanics

A simplified version of White's Density Matrix Renormalization Group (DMRG) algorithm has been used to find the ground state of the free particle on a tight-binding lattice. We generalize this algorithm to treat the tight-binding particle in an arbitrary potential and to find excited states. We thereby solve a discretized version of the single-particle Schr\"odinger equation, which we can then take to the continuum limit. This allows us to obtain very accurate results for the lowest energy levels of the quantum harmonic oscillator, anharmonic oscillator and double-well potential. We compare the DMRG results thus obtained with those achieved by other methods.Comment: REVTEX file, 21 pages, 3 Tables, 4 eps Figure

Charge order induced by electron-lattice interaction in NaV2O5

We present Density Matrix Renormalization Group calculations of the ground-state properties of quarter-filled ladders including static electron-lattice coupling. Isolated ladders and two coupled ladders are considered, with model parameters obtained from band-structure calculations for $\alpha^\prime$-NaV$_2$O$_5$. The relevant Holstein coupling to the lattice causes static out-of-plane lattice distortions, which appear concurrently with a charge-ordered state and which exhibit the same zigzag pattern observed in experiments. The inclusion of electron-lattice coupling drastically reduces the critical nearest-neighbor Coulomb repulsion $V_c$ needed to obtain the charge-ordered state. No spin gap is present in the ordered phase. The charge ordering is driven by the Coulomb repulsion and the electron-lattice interaction. With electron-lattice interaction, coupling two ladders has virtually no effect on $V_c$ or on the characteristics of the charge-ordered phase. At V=0.46\eV, a value consistent with previous estimates, the lattice distortion, charge gap, charge order parameter, and the effective spin coupling are in good agreement with experimental data for NaV$_2$O_5$.Comment: 7 pages, 9 figure

Quantum criticality of dipolar spin chains

We show that a chain of Heisenberg spins interacting with long-range dipolar forces in a magnetic field h perpendicular to the chain exhibits a quantum critical point belonging to the two-dimensional Ising universality class. Within linear spin-wave theory the magnon dispersion for small momenta k is [Delta^2 + v_k^2 k^2]^{1/2}, where Delta^2 \propto |h - h_c| and v_k^2 \propto |ln k|. For fields close to h_c linear spin-wave theory breaks down and we investigate the system using density-matrix and functional renormalization group methods. The Ginzburg regime where non-Gaussian fluctuations are important is found to be rather narrow on the ordered side of the transition, and very broad on the disordered side.Comment: 6 pages, 5 figure

Coherent matter waves emerging from Mott-insulators

We study the formation of (quasi-)coherent matter waves emerging from a Mott insulator for strongly interacting bosons on a one-dimensional lattice. It has been shown previously that a quasi-condensate emerges at momentum k=\pi/2a, where a is the lattice constant, in the limit of infinitely strong repulsion (hard-core bosons). Here we show that this phenomenon persists for all values of the repulsive interaction that lead to a Mott insulator at a commensurate filling. The non-equilibrium dynamics of hard-core bosons is treated exactly by means of a Jordan-Wigner transformation, and the generic case is studied using a time-dependent density matrix renormalization group technique. Different methods for controlling the emerging matter wave are discussed.Comment: 20 pages, 11 figures. Published versio

Float zone experiments in space

The molten zone/freezing crystal interface system and all the mechanisms were examined. If Marangoni convection produces oscillatory flows in the float zone of semiconductor materials, such as silicon, then it is unlikely that superior quality crystals can be grown in space using this process. The major goals were: (1) to determine the conditions for the onset of Marangoni flows in molten tin, a model system for low Prandtl number molten semiconductor materials; (2) to determine whether the flows can be suppressed by a thin oxide layer; and (3) based on experimental and mathematical analysis, to predict whether oscillatory flows will occur in the float zone silicon geometry in space, and if so, could it be suppressed by thin oxide or nitride films. Techniques were developed to analyze molten tin surfaces in a UHV system in a disk float zone geometry to minimize buoyancy flows. The critical Marangoni number for onset of oscillatory flows was determined to be greater than 4300 on atomically clean molten tin surfaces