Germán Sierra

Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings

N = 4 supersymmetric Yang-Mills operators carrying large charges are dual to semi- classical strings in AdS5 × S 5 . The spectrum of anomalous dimensions of very large oper- ators has been calculated solving the Bethe ansatz equations in the thermodynamic limit, and matched to energies of string solitons. We have considered finite size corrections to the Bethe equations, that should correspond to quantum effects on the string side.

EQUIVALENCE OF THE VARIATIONAL MATRIX PRODUCT METHOD AND THE DENSITY MATRIX RENORMALIZATION GROUP APPLIED TO SPIN CHAINS

We study the relationship between the Density Matrix Renormalization Group (DMRG) and the variational matrix product method (MPM). In the latter method one can also define a density matrix whose eigenvalues turn out to be numerically close to those of the DMRG. We illustrate our ideas with the spin-1 Heisenberg chain, where we compute the ground-state energy and the spin correlation length. We also give a rotational invariant formulation of the MPM.

Entanglement of low-energy excitations in Conformal Field Theory

In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low-lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and Rényi entropies of the ground state, which display a universal logarithmic behavior depending on the central charge. In this Letter we generalize this result to those excited states of the chain that correspond to primary fields in CFT. It is shown that the nth Rényi entropy is related to a 2n-point correlator of primary fields. We verify this statement for the critical XX and XXZ chains. This result uncovers a new link between quantum information theory and CFT.

The quantum symmetry of rational conformal field theories

The quantum group symmetry of the c

Quantum group meaning of the Coulomb gas

1 Rational Conformal Field Theory, in its Coulomb gas version, is formulated in terms of a new type of screened vertex operators, which define the representation spaces of a quantum group Q. The conformal properties of these operators show a deep interplay between the quantum group Q and the Virasoro algebra. The R-matrix, the comultiplication rules and the quantum Clebsch-Gordan coefficients of Q are obtained using contour deformation techniques. Finally, the relation between the chiral vertex operators and the quantum Clebsch-Gordan coefficients is shown.

Density Matrix Renormalization Group Study of Ultrasmall Superconducting Grains

The quantum group symmetry is realized in the Coulomb gas version of the C < 1 models. We define the representation spaces of the quantum group in terms of screened vertex operators and we interpret the number of screening operators as the genuine quantum group number. Contour deformation yields the quantum R-matrix and the decomposition rule yields the quantum Clebsch-Gordan coefficients and the conformal blocks which are the invariant tensors of the quantized symmetry.

Large-N limit of the exactly solvable BCS model: analytics versus numerics

This work was supported by the DGES Spanish Grants No. PB95-01123 (J. D.) and No. PB97-1190 (G. S.).

Russian doll renormalization group and superconductivity

Abstract We have studied the numerical solutions of Richardson equations of the BCS model in the limit of large number of energy levels at half-filling, and compare them with the analytic results derived by Gaudin and Richardson, which in turn leads to the standard BCS solution. We focus on the location and density of the roots, the eigenvalues of the conserved quantities, and the scaling properties of the total energy for the equally spaced and the two-level models.

The nonlinear sigma model and spin ladders

We show that a simple extension of the standard BCS Hamiltonian leads to an infinite number of BCS eigenstates with different energy gaps and self-similar properties, described by a cyclic renormalization group flow of the BCS coupling constant which returns to its original value after a finite renormalization group time.

Entanglement of excited states in critical spin chains

The well known Haldane map from spin chains into the O(3) nonlinear sigma model is generalized to the case of spin ladders. This map allows us to explain the different qualitative behaviour between even and odd ladders, in exactly the same way as it explains the difference between integer and half-integer spin chains. Namely, for even ladders the topological term in the sigma model action is absent, while for odd ladders the parameter, which multiplies the topological term, is equal to , where S is the spin of the ladder. Hence even ladders should have a dynamically generated spin gap, while odd ladders with half-integer spin should stay gapless and physically equivalent to a perturbed Wess - Zumino - Witten model in the infrared regime. We also derive some consequences from the dependence of the sigma model coupling constant on the ladder Heisenberg couplings constants.