Quantum spin chains of Temperley-Lieb type: periodic boundary conditions, spectral multiplicities and finite temperature

We determine the spectra of a class of quantum spin chains of Temperley-Lieb type by utilizing the concept of Temperley-Lieb equivalence with the S=1/2 XXZ chain as a reference system. We consider open boundary conditions and in particular periodic boundary conditions. For both types of boundaries the identification with XXZ spectra is performed within isomorphic representations of the underlying Temperley-Lieb algebra. For open boundaries the spectra of these models differ from the spectrum of the associated XXZ chain only in the multiplicities of the eigenvalues. The periodic case is rather different. Here we show how the spectrum is obtained sector-wise from the spectra of globally twisted XXZ chains. As a spin-off, we obtain a compact formula for the degeneracy of the momentum operator eigenvalues. Our representation theoretical results allow for the study of the thermodynamics by establishing a TL-equivalence at finite temperature and finite field.Comment: 29 pages, LaTeX, two references added, redundant figures remove

On the Uq[sl(2)]{\cal{U}}_{q}[sl(2)] Temperley-Lieb reflection matrices

This work concerns the boundary integrability of the spin-s ${\cal{U}}_{q}[sl(2)]$ Temperley-Lieb model. A systematic computation method is used to constructed the solutions of the boundary Yang-Baxter equations. For $s$ half-integer, a general $2s(s+1)+3/2$ free parameter solution is presented. It turns that for $s$ integer, the general solution has $2s(s+1)+1$ free parameters. Moreover, some particular solutions are discussed.Comment: LaTex 17 page

Bifurcations, order, and chaos in the Bose-Einstein condensation of dipolar gases

We apply a variational technique to solve the time-dependent Gross-Pitaevskii equation for Bose-Einstein condensates in which an additional dipole-dipole interaction between the atoms is present with the goal of modelling the dynamics of such condensates. We show that universal stability thresholds for the collapse of the condensates correspond to bifurcation points where always two stationary solutions of the Gross-Pitaevskii equation disappear in a tangent bifurcation, one dynamically stable and the other unstable. We point out that the thresholds also correspond to "exceptional points," i.e. branching singularities of the Hamiltonian. We analyse the dynamics of excited condensate wave functions via Poincare surfaces of section for the condensate parameters and find both regular and chaotic motion, corresponding to (quasi-) periodically oscillating and irregularly fluctuating condensates, respectively. Stable islands are found to persist up to energies well above the saddle point of the mean-field energy, alongside with collapsing modes. The results are applicable when the shape of the condensate is axisymmetric.Comment: 10 pages, 4 figures, minor changes in the text and additional reference adde

Scaling limit of the one-dimensional attractive Hubbard model: The half-filled band case

The scaling limit of the higher level Bethe Ansatz (HLBA) equations for a macroscopically half-filled Hubbard chain is considered. These equations practically decouple into three disjoint sets which are again of the BA type, and correspond to the secular equations of three different kinds of dressed particles (one massive and two massless). The finite size corrections and the fine structure of the spectrum show that the massless sector corresponds to a conformal field with central charge c=1 and Gaussian anomalous dimensions. The zero temperature free energy is also calculated and is found to be in perfect agreement with the results of a perturbative calculation in the SU(2) chiral Gross-Neveu (CGN) model.Comment: LATEX, uses Revtex, 39 page

Scattering and Thermodynamics of Integrable N=2 Theories

We study $N$=2 supersymmetric integrable theories with spontaneously-broken \Zn\ symmetry. They have exact soliton masses given by the affine $SU(n)$ Toda masses and fractional fermion numbers given by multiples of $1/n$. The basic such $N$=2 integrable theory is the $A_n$-type $N$=2 minimal model perturbed by the most relevant operator. The soliton content and exact S-matrices are obtained using the Landau-Ginzburg description. We study the thermodynamics of these theories and calculate the ground-state energies exactly, verifying that they have the correct conformal limits. We conjecture that the soliton content and S-matrices in other integrable \Zn\ $N$=2 theories are given by the tensor product of the above basic $N$=2 \Zn\ scattering theory with various $N$=0 theories. In particular, we consider integrable perturbations of $N$=2 Kazama-Suzuki models described by generalized Chebyshev potentials, $CP^{n-1}$ sigma models, and $N$=2 sine-Gordon and its affine Toda generalizations.Comment: 31 page

Statistical Models with a Line of Defect

The factorization condition for the scattering amplitudes of an integrable model with a line of defect gives rise to a set of Reflection-Transmission equations. The solutions of these equations in the case of diagonal $S$-matrix in the bulk are only those with $S =\pm 1$. The choice $S=-1$ corresponds to the Ising model. We compute the transmission and reflection amplitudes relative to the interaction of the Majorana fermion with the defect and we discuss their relevant features.Comment: 14 pages, LATEX file, ISAS/EP/94/30 (Figures added, originally missed for E-mail transmission problem.

Fungal Chitin Dampens Inflammation through IL-10 Induction Mediated by NOD2 and TLR9 Activation

Funding: JW and NARG thank the Wellcome Trust (080088, 086827, 075470), The Wellcome Trust Strategic Award in Medical Mycology and Fungal Immunology (097377) and the European Union ALLFUN (FP7/2007 2013, HEALTH-2010-260338) for funding. MGN was supported by a Vici grant of the Netherlands Organisation for Scientific Research. AJPB and DMM were funded by STRIFE, ERC-2009-AdG-249793 and AJPB additionally by FINSysB, PITN-GA-2008-214004 and the BBSRC [BB/F00513X/1]. MDL was supported by the MRC (MR/J008230/1). GDB and SV were funded by the Wellcome Trust (086558) and TB and MK were funded by the Deutsche Forschungsgemeinschaft (Bi 696/3-1; Bi 696/5-2; Bi 696/10-1). MS was supported by the Deutsche Forschungsgemeinschaft (Sch 897/1-3) and the National Institute of Dental and Craniofacial Research (R01 DE017514-01). TDK and RKSM were funded by the National Institute of Health (AR056296, AI101935) and the American Lebanese Syrian Associated Charities (ALSAC). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD

Correlation Functions in 2-Dimensional Integrable Quantum Field Theories

In this talk I discuss the form factor approach used to compute correlation functions of integrable models in two dimensions. The Sinh-Gordon model is our basic example. Using Watson's and the recursive equations satisfied by matrix elements of local operators, I present the computation of the form factors of the elementary field $\phi(x)$ and the stress-energy tensor $T_{\mu\nu}(x)$ of the theory.Comment: 19pp, LATEX version, (talk at Como Conference on ``Integrable Quantum Field Theories''