Search results for "transfer matrix"
showing 10 items of 30 documents
Exact solution of the 1D Hubbard model with NN and NNN interactions in the narrow-band limit
2013
We present the exact solution, obtained by means of the Transfer Matrix (TM) method, of the 1D Hubbard model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) Coulomb interactions in the atomic limit (t=0). The competition among the interactions ($U$, $V_1$, and $V_2$) generates a plethora of T=0 phases in the whole range of fillings. $U$, $V_1$, and $V_2$ are the intensities of the local, NN and NNN interactions, respectively. We report the T=0 phase diagram, in which the phases are classified according to the behavior of the principal correlation functions, and reconstruct a representative electronic configuration for each phase. In order to do that, we make an analytic limit $T\…
The effect of disorder on optical spectra of conjugated polymers
1993
Abstract Using the semi-empirical parametrization of the Pariser-Parr-Pople model we determine the excitonic states in conjugated polymers. The employed parameters correspond to a moderate strength of the long-range Coulomb interaction. In order to take the disorder into account, the nearest-neighbour transfer matrix elements are chosen according to a random distribution. Averaging the results over a large number of chains of 100 sites, which are known to be sufficiently long so that finite-size effects become negligible, we obtain the linear and third-order nonlinear optical susceptibilities. With increasing disorder the linear absorption, the two-photon absorption and the third-harmonic g…
Critical behavior of short range Potts glasses
1993
We study by means of Monte Carlo simulations and the numerical transfer matrix technique the critical behavior of the short rangep=3 state Potts glass model in dimensionsd=2,3,4 with both Gaussian and bimodal (±J) nearest neighbor interactions on hypercubic lattices employing finite size scaling ideas. Ind=2 in addition the degeneracy of the glass ground state is computed as a function of the number of Potts states forp=3, 4, 5 and compared to that of the antiferromagnetic ground state. Our data indicate a transition into a glass phase atT=0 ind=2 with an algebraic singularity, aT=0 transition ind=3 with an essential singularity of the form χ∼exp(const.T−2), and an algebraic singularity atT…
Bloch analysis of finite periodic microring chains
2005
We apply Bloch analysis to the study of finite periodic cascading of microring resonators. Diagonalization of the standard transfer matrix approach not only allows to find an exact analytic expression for transmission and reflection, but also to derive a closed form solution for the field in every point of the structure. To give more physical insight we analyze the main features of the transmission resonances in a finite chain and we give some hints for their experimental verification
Numerical studies of Minimally Doubled Fermions
2013
We have performed the first numerical study of minimally doubled fermions of the Karsten-Wilczek class in the quenched approximation. This requires fixing the counterterms, which arise due to hypercubic symmetry breaking induced by the Karsten-Wilczek term. Non-perturbative renormalisation criteria are formulated after a detailed study of the parameter dependence of mesonic observables. Minimisation of the mass anisotropy of the pseudoscalar ground state fixes non-perturbative renormalisation conditions for the counterterm coefficients. These anisotropies are mapped out by probing different euclidean components of the transfer matrix through calculations of the pseudoscalar ground state mas…
FINITE-SIZE CORRECTIONS TO CORRELATION FUNCTION AND SUSCEPTIBILITY IN 2D ISING MODEL
2006
Transfer matrix calculations of the critical two-point correlation function in 2D Ising model on a finite-size [Formula: see text] lattice with periodic boundaries along 〈11〉 direction are extended to L = 21. A refined analysis of the correlation function in 〈10〉 crystallographic direction at the distance r = L indicates the existence of a nontrivial finite-size correction of a very small amplitude with correction-to-scaling exponent ω < 2 in agreement with our foregoing study for L ≤ 20. Here we provide an additional evidence and show that amplitude a of the multiplicative correction term 1 + aL-ωis about -3.5·10-8if ω = 1/4 (the expected value). We calculate also the susceptibility for…
Universality classes for wetting in two-dimensional random-bond systems
1991
Interface-unbinding transitions, such as those arising in wetting phenomena, are studied in two-dimensional systems with quenched random impurities and general interactions. Three distinct universality classes or scaling regimes are investigated using scaling arguments and extensive transfer-matrix calculations. Both the critical exponents and the critical amplitudes are determined for the weak- and the strong-fluctuation regime. In the borderline case of the intermediate-fluctuation regime, the asymptotic regime is not accessible to numerical simulations. We also find strong evidence for a nontrivial delocalization transition of an interface that is pinned to a line of defects.
Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables
2014
28 pages; International audience; We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains. The corresponding homogeneous limit reproduces the spectrum of the Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most general integrable boundaries. The spectrum is characterized by a second order finite difference functional equation of Baxter type with an inhomogeneous term which vanishes only for some special but yet interesting non-diagonal boundary conditions. This functional equation is shown to…
SOV approach for integrable quantum models associated to general representations on spin-1/2 chains of the 8-vertex reflection algebra
2013
The analysis of the transfer matrices associated to the most general representations of the 8-vertex reflection algebra on spin-1/2 chains is here implemented by introducing a quantum separation of variables (SOV) method which generalizes to these integrable quantum models the method first introduced by Sklyanin. More in detail, for the representations reproducing in their homogeneous limits the open XYZ spin-1/2 quantum chains with the most general integrable boundary conditions, we explicitly construct representations of the 8-vertex reflection algebras for which the transfer matrix spectral problem is separated. Then, in these SOV representations we get the complete characterization of t…
Generalized curved beam on elastic foundation solved by Transfer Matrix Method
2011
A solution of space curved bars with generalized Winkler soil found by means of Transfer Matrix Method is presented. Distributed, concentrated loads and imposed strains are applied to the beam as well as rigid or elastic boundaries are considered at the ends. The proposed approach gives the analytical and numerical exact solution for circular beams and rings, loaded in the plane or perpendicular to it. A well-approximated solution can be found for general space curved bars with complex geometry. Elastic foundation is characterized by six parameters of stiffness in different directions: three for rectilinear springs and three for rotational springs. The beam has axial, shear, bending and tor…