The exact equivalence of the two-flavour strong coupling lattice Schwinger model with Wilson fermions to a vertex model

In this paper a method previously employed by Salmhofer to establish an exact equivalence of the one-flavour strong coupling lattice Schwinger model with Wilson fermions to some 8-vertex model is applied to the case with two flavours. As this method is fairly general and can be applied to strong coupling QED and purely fermionic models with any (sufficiently small) number of Wilson fermions in any dimension the purpose of the present study is mainly a methodical one in order to gain some further experience with it. In the paper the vertex model equivalent to the two-flavour strong coupling lattice Schwinger model with Wilson fermions is found. It turns out to be some modified 3-state 20-vertex model on the square lattice, which can also be understood as a regular 6-state vertex model. In analogy with the one- flavour case, this model can be viewed as some loop model.Comment: 22 pages LaTe

The exact equivalence of the one-flavour lattice Thirring model with Wilson fermions to a two-colour loop model

Within Euclidean lattice field theory an exact equivalence between the one-flavour 2D Thirring model with Wilson fermions and Wilson parameter $r = 1$ to a two-colour loop model on the square lattice is established. For non-interacting fermions this model reduces to an exactly solved loop model which is known to be a free fermion model. The two-colour loop model equivalent to the Thirring model can also be understood as a 4-state 49-vertex model.Comment: 29 pages LaTe

Long-Time Tails and Anomalous Slowing Down in the Relaxation of Spatially Inhomogeneous Excitations in Quantum Spin Chains

Exact analytic calculations in spin-1/2 XY chains, show the presence of long-time tails in the asymptotic dynamics of spatially inhomogeneous excitations. The decay of inhomogeneities, for $t\to \infty$, is given in the form of a power law $$(t/\tau_{Q}) ^{-\nu_{Q}}$$ where the relaxation time $\tau_{Q}$ and the exponent $\nu_{Q}$ depend on the wave vector $Q$, characterizing the spatial modulation of the initial excitation. We consider several variants of the XY model (dimerized, with staggered magnetic field, with bond alternation, and with isotropic and uniform interactions), that are grouped into two families, whether the energy spectrum has a gap or not. Once the initial condition is given, the non-equilibrium problem for the magnetization is solved in closed form, without any other assumption. The long-time behavior for $t\to \infty$ can be obtained systematically in a form of an asymptotic series through the stationary phase method. We found that gapped models show critical behavior with respect to $Q$, in the sense that there exist critical values $Q_{c}$, where the relaxation time $\tau_{Q}$ diverges and the exponent $\nu_{Q}$ changes discontinuously. At those points, a slowing down of the relaxation process is induced, similarly to phenomena occurring near phase transitions. Long-lived excitations are identified as incommensurate spin density waves that emerge in systems undergoing the Peierls transition. In contrast, gapless models do not present the above anomalies as a function of the wave vector $Q$.Comment: 25 pages, 2 postscript figures. Manuscript submitted to Physical Review

Supersymmetric t-J Gaudin Models and KZ Equations

Supersymmetric t-J Gaudin models with both periodic and open boundary conditions are constructed and diagonalized by means of the algebraic Bethe ansatz method. Off-shell Bethe ansatz equations of the Gaudin systems are derived, and used to construct and solve the KZ equations associated with $sl(2|1)^{(1)}$ superalgebra.Comment: LaTex 21 page

Dynamic properties of the spin-1/2 XY chain with three-site interactions

We consider a spin-1/2 XY chain in a transverse (z) field with multi-site interactions. The additional terms introduced into the Hamiltonian involve products of spin components related to three adjacent sites. A Jordan-Wigner transformation leads to a simple bilinear Fermi form for the resulting Hamiltonian and hence the spin model admits a rigorous analysis. We point out the close relationships between several variants of the model which were discussed separately in previous studies. The ground-state phases (ferromagnet and two kinds of spin liquid) of the model are reflected in the dynamic structure factors of the spin chains, which are the main focus in this study. First we consider the zz dynamic structure factor reporting for this quantity a closed-form expression and analyzing the properties of the two-fermion (particle-hole) excitation continuum which governs the dynamics of transverse spin component fluctuations and of some other local operator fluctuations. Then we examine the xx dynamic structure factor which is governed by many-fermion excitations, reporting both analytical and numerical results. We discuss some easily recognized features of the dynamic structure factors which are signatures for the presence of the three-site interactions.Comment: 28 pages, 10 fugure

Transcatheter Therapies for the Treatment of Valvular and Paravalvular Regurgitation in Acquired and Congenital Valvular Heart Disease

AbstractTranscatheter therapies in structural heart disease have evolved tremendously over the past 15 years. Since the introduction of the first balloon-expandable valves for stenotic lesions with implantation in the pulmonic position in 2000, treatment for valvular heart disease in the outflow position has become more refined, with newer-generation devices, alternative techniques, and novel access approaches. Recent efforts into the inflow position and regurgitant lesions, with transcatheter repair and replacement technologies, have expanded our potential to treat a broader, more heterogeneous patient population. The evolution of multimodality imaging has paralleled these developments. Three- and 4-dimensional visualization and concomitant use of novel technologies, such as fusion imaging, have supported technical growth, from pre-procedural planning and intraprocedural guidance, to assessment of acute results and follow-up. A multimodality approach has allowed operators to overcome many limitations of each modality and facilitated integration of a multidisciplinary team for treatment of this complex patient population