Generalization of the U_q(gl(N)) algebra and staggered models

We develop a technique of construction of integrable models with a Z_2 grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang-Baxter Equations are written down and their solution for the gl(N) case are found. We analyze in details the N=2 case and find the corresponding quantum group behind this solution. It can be regarded as quantum U_{q,B}(gl(2)) group with a matrix deformation parameter qB with (qB)^2=q^2. The symmetry behind these models can also be interpreted as the tensor product of the (-1)-Weyl algebra by an extension of U_q(gl(N)) with a Cartan generator related to deformation parameter -1.Comment: 12 pages ; Latex2

Absence of extended states in a ladder model of DNA

We consider a ladder model of DNA for describing carrier transport in a fully coherent regime through finite segments. A single orbital is associated to each base, and both interstrand and intrastrand overlaps are considered within the nearest-neighbor approximation. Conduction through the sugar-phosphate backbone is neglected. We study analytically and numerically the spatial extend of the corresponding states by means of the Landauer and Lyapunov exponents. We conclude that intrinsic-DNA correlations, arising from the natural base pairing, does not suffice to observe extended states, in contrast to previous claims.Comment: 4 RevTex pages, 4 figures include

Electron states in a one-dimensional random binary alloy

We present a model for alloys of compound semiconductors by introducing a one-dimensional binary random system where impurities are placed in one sublattice while host atoms lie on the other sublattice. The source of disorder is the stochastic fluctuation of the impurity energy from site to site. Although the system is one-dimensional and random, we demonstrate analytical and numerically the existence of extended states in the neighborhood of a given resonant energy, which match that of the host atoms.Comment: 11 pages, REVTeX, 3 PostScript figure

Integrable XYZ Model with Staggered Anisotropy Parameter

We apply to the XYZ model the technique of construction of integrable models with staggered parameters, presented recently for the XXZ case. The solution of modified Yang-Baxter equations is found and the corresponding integrable zig-zag ladder Hamiltonian is calculated. The result is coinciding with the XXZ case in the appropriate limit.Comment: 8 pages ; epic packag

Hofstadter Problem on the Honeycomb and Triangular Lattices: Bethe Ansatz Solution

We consider Bloch electrons on the honeycomb lattice under a uniform magnetic field with $2 \pi p/q$ flux per cell. It is shown that the problem factorizes to two triangular lattices. Treating magnetic translations as Heisenberg-Weyl group and by the use of its irreducible representation on the space of theta functions, we find a nested set of Bethe equations, which determine the eigenstates and energy spectrum. The Bethe equations have simple form which allows to consider them further in the limit $p, q \to \infty$ by the technique of Thermodynamic Bethe Ansatz and analyze Hofstadter problem for the irrational flux.Comment: 7 pages, 2 figures, Revte

An Integrable Model with non-reducible three particle R-Matrix

We define an integrable lattice model which, in the notation of Yang, in addition to the conventional 2-particle $R$-matrices also contains non-reducible 3-particle $R$-matrices. The corresponding modified Yang-Baxter equations are solved and an expression for the transfer matrix is found as a normal ordered exponential of a (non-local) Hamiltonian.Comment: 13 pages, 4 figure

Localization-delocalization transition in the quasi-one-dimensional ladder chain with correlated disorder

The generalization of the dimer model on a two-leg ladder is defined and investigated both, analytically and numerically. For the closed system we calculate the Landauer resistance analytically and found the presence of the point of delocalization at the band center which is confirmed by the numerical calculations of the Lyapunov exponent. We calculate also analytically the localization length index and present the numerical investigations of the density of states (DOS). For the open counterpart of this model the distribution of the Wigner delay times is calculated numerically. It is shown how the localization-delocalization transition manifest itself in the behavior of the distribution.Comment: 9 pages, 10 figures, Revte

Grassmann-Gaussian integrals and generalized star products

In quantum scattering on networks there is a non-linear composition rule for on-shell scattering matrices which serves as a replacement for the multiplicative rule of transfer matrices valid in other physical contexts. In this article, we show how this composition rule is obtained using Berezin integration theory with Grassmann variables.Comment: 14 pages, 2 figures. In memory of Al.B. Zamolodichiko

Note on the thermodynamic Bethe Ansatz approach to the quantum phase diagram of the strong coupling ladder compounds

We investigate the low-temperature phase diagram of the exactly solved su(4) two-leg spin ladder as a function of the rung coupling $J_{\perp}$ and magnetic field $H$ by means of the thermodynamic Bethe Ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases, while in the presence of a strong magnetic field there is no singlet ground state for ferromagnetic rung coupling. For antiferromagnetic rung coupling, there is a gapped phase in the regime H H_{c2} and a Luttinger liquid magnetic phase in the regime H_{c1} < H < H_{c2}. The critical behaviour derived using the TBA is consistent with the existing experimental, numerical and perturbative results for the strong coupling ladder compounds. This includes the spin excitation gap and the critical fields H_{c1} and H_{c2}, which are in excellent agreement with the experimental values for the known strong coupling ladder compounds (5IAP)_2CuBr_4 2H_2 O, Cu_2(C_5 H_{12} N_2)_2 Cl_4 and (C_5 H_{12} N)_2 CuBr_4. In addition we predict the spin gap $\Delta \approx J_{\perp}-{1/2}J_{\parallel}$ for the weak coupling compounds with $J_{\perp} \sim J_{\parallel}$, such as (VO)_2 P_2 O_7, and also show that the gap opens for arbitrary $J_{\perp}/ J_{\parallel}$.Comment: 10 pages, 3 figure