Titanate nanotubes Na(2-x)H(x)Ti(3)O(7) produced by alkali hydrothermally treated ground TiO(2) aerogels are investigated as possible materials for high-temperature thermoelectric conversion by measuring their thermoelectric properties. Strikingly, the Seebeck coefficients increased sharply in the temperature range 745 to 1032 K, reaching a maximum of 302 muV/K. The electrical resistivity of the TNNTs ranged from 325 to 525 Omegam, which is lower than that of bulk TiO(2), and thermal conductivities at room temperature were also very low, ranging from 0.55 to 0.75 Wm(-1) K(-1). The hollow structure of the titanate nanotubes, with small, uniform diameters, is thought to be responsible for the ultralow thermal conductivity. The large thermoelectric power and ultralow thermal conductivity suggest that titanate nanotubes represent a new kind of p-type oxide thermoelectric material.

We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SUð3Þ 1 Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit. DOI: 10.1103/PhysRevLett.114.145301 PACS numbers: 67.85.-d, 03.65.Ud, 11.25.Hf, 65.40.gd Cold atomic gases in optical lattices have become an ideal framework for studying quantum many-body systems in recent years [1]. In particular, various schemes have been proposed to study quantum magnetism [2]. For spin 1=2 systems, simulation of the Ising model has been realized using bosons in a tilted optical lattice [3]. It has also been proposed that the spin 1=2 XYZ Heisenberg model can be realized using p-orbital bosons [4]. This rapid progress in cold atomic physics results in a considerable renewal of interest to study models with higher spins or higher symmetries, especially for models that are potentially realizable by cold atomic systems. A natural direction is to study spinor bosons and their novel phases. For example, it has been proposed that the spin-1 bilinear biquadractic (BB) model can be engineered using spin-1 cold bosons in an optical lattice [5,6]. Furthermore, the phase diagram of spin-1 bosons in a one-dimensional (1D) lattice has been studied numerically and compared to the spin-1 BB model [7]. Since spin-2 bosons are available and have been experimentally studied [8][9][10][11], it is of great interest to explore the phases realizable by spin-2 bosons. On the other hand, it has also been pointed out that fermions with hyperfine spin F ¼ 3=2 can be used to realize models with SO(5) symmetry [12], or to realize an SU(3) spin chain by effectively suppressing the occupation of one of the middle states [13]. Possibilities to realize higher SU(N) symmetry have also been proposed [14,15]. Along this line, spin dynamics and correlation have been studied experimentally using cold fermions with effective spin ranging from 1=2 to 9=2 [16,17]. Another interesting problem is to explore symmetries that emerge in the low energy limit of the models. Indeed, different aspects of emergent symmetries have been discussed widely in the recent literature. Examples include SO(5) and SO (8) symmetries in high temperature superconductors and two-leg ladders [18,19] Recently we studied the phase diagram of spin-2 bosons in a 1D optical lattice with one particle per site and identified three possible phases for a finite system: ferromagnetic, dimerized, and trimerized phases [25]. Within the trimerized phase, if the system size is a multiple of 3, the ground state is a spin singlet with a finite-siz...

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We present our proposals for generating total hyperfine spin zero state for two f = 1 or two f = 2 particles, starting from initial unentangled states. We show that our goal can be achieved by exploiting spin changing dynamics and quadratic Zeeman shifts with realistic choices of external magnetic fields and evolution time intervals.

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