arXiv subjects

German Sierra

Publications and source records attributed to German Sierra.

58 records · Page 4Linked to original sources

arXiv1995

Real Space Renormalization Group Methods and Quantum Groups

We apply real-space RG methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field defined in an open chain with appropiate boundary terms. The quantum group symmetry is preserved under the RG transformation except for the appearence of a quantum group anomalous term which vanishes in the classical case. We obtain correctly the line of critical XXZ models. In the ITF model the RG-flow coincides with the tensor product decomposition of cyclic irreps. of $SU_q(2)$ with $q^4=1$.

cond-mat↗

arXiv1995

Strongly Interacting Spinless Fermions in D=1 and 2 Dimensions: A Perturbative-Variational Approach

We propose a perturbative-variational approach to interacting fermion systems on 1D and 2D lattices at half-filling. We address relevant issues such as the existence of Long Range Order, quantum phase transitions and the evaluation of ground state energy. In 1D our method is capable of unveiling the existence of a critical point in the coupling constant at $(t/U)_c=0.7483$ as in fact occurs in the exact solution at a value of 0.5. In our approach this phase transition is described as an example of Bifurcation Phenomena in the variational computation of the ground state energy. In 2D the van Hove singularity plays an essential role in changing the asymptotic behaviour of the system for large values of $t/U$. In particular, the staggered magnetization for large $t/U$ does not display the Hartree-Fock law $(t/U) e^{-2 π\sqrt{t/U}}$ but instead we find the law $(t/U) e^{- \frac{π^2}{3} t/U}$. Moreover, the system does not exhibit bifurcation phenomena and thus we do not find a critical point separating a CDW state from a fermion "liquid" state.

cond-mat↗

arXiv1992

A brief history of hidden quantum symmetries in Conformal Field Theories

We review briefly a stream of ideas concerning the role of quantum groups as hidden symmetries in conformal field theories, paying particular attention to the field theoretical representations of quantum groups based on Coulomb gas methods. An extensive bibliography is also included.

hep-th↗

arXiv1991

A New Solution to the Star--Triangle Equation Based on U$_q$(sl(2)) at Roots of Unit

We find new solutions to the Yang--Baxter equation in terms of the intertwiner matrix for semi-cyclic representations of the quantum group $U_q(s\ell(2))$ with $q= e^{2πi/N}$. These intertwiners serve to define the Boltzmann weights of a lattice model, which shares some similarities with the chiral Potts model. An alternative interpretation of these Boltzmann weights is as scattering matrices of solitonic structures whose kinematics is entirely governed by the quantum group. Finally, we consider the limit $N\to\infty$ where we find an infinite--dimensional representation of the braid group, which may give rise to an invariant of knots and links.

hep-th↗