Francisco C. Alcaraz

Surface exponents of the quantum XXZ, Ashkin-Teller and Potts models

Eigenspectra of the critical quantum Ashkin-Teller and Potts chains with free boundaries can be obtained from that of the XXZ chain with free boundaries and a complex surface field. By deriving and solving numerically the Bethe ansatz equations for such boundaries the authors obtain eigenenergies of XXZ chains of up to 512 sites. The conformal anomaly and surface exponents of the quantum XXZ, Ashkin-Teller, and Potts chains are calculated by exploiting their relations with the mass gap amplitudes as predicted by conformal invariance.

Reaction-Diffusion Processes, Critical Dynamics, and Quantum Chains

Abstract The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schrodinger equation in which the wave function is the probability distribution and the Hamiltonian is that of a quantum chain with nearest neighbor interactions. Since many one-dimensional quantum chains are integrable, this opens a new field of applications. At the same time physical intuition and probabilistic methods bring new insight into the understanding of the properties of quantum chains. A simple example is the asymmetric diffusion of several species of particles which leads naturally to Hecke algebras and q -deformed quantum groups. Many other examples are given. Several relevant technical aspects like critical exponents, correlation functions, and finite-size scaling are also discussed in detail.

Conformal invariance, the XXZ chain and the operator content of two-dimensional critical systems

Abstract The massless regime of the quantum XXZ chain is an example of a conformally invariant (1 + 1)-dimensional Hamiltonian with conformal anomaly c = 1. In this paper, Bethe ansatz equations are formulated and solved numerically for eigenstates of the XXZ Hamiltonian on a finite chain with periodic boundary conditions and with a generalized class of “twisted” boundary conditions. The resulting spectra are found to be in accord with predictions of conformal invariance and the corresponding operator content is identified. With periodic boundary conditions, eight-vertex and Gaussian model operators are found. With the twisted boundary conditions, operators from the operator algebras of the Ashkin-Teller and q -state Potts models are identified. This identification is achieved by constructing exact equivalences between eigenergies of the quantum Ashkin-Teller and Potts Hamiltonians with periodic boundary conditions and levels of the XXZ Hamiltonian with modified boundary conditions. In the Potts case, states in the ground-state sector correspond exactly to states of the XXZ chain with a “defect seam.” The effect of this seam on the ground-state energy is shown to generate the conformal anomaly of the Potts model. For the 4-state model, the XXZ equivalence is used to perform very large lattice calculations and, thereby, to obtain direct confirmation of the expected values for its critical exponents. Finally, the leading finite-size corrections to the predictions of conformal invariance are analyzed and the dominant irrelevant operators governing these corrections identified.

Critical behavior of the spin- 3 2 Blume-Capel model in two dimensions

The phase diagram of the spin-3/2 Blume-Capel model in two dimensions is explored by conventional finite-size scaling, conformal invariance and Monte Carlo simulations. The model in its

Entanglement of low-energy excitations in Conformal Field Theory

\tau

FREE-FERMION ENERGIES IN THE SU(N) PERK-SCHULTZ MODEL

-continuum Hamiltonian version is also considered and compared with others spin-3/2 quantum chains. Our results indicate that differently from the standard spin-1 Blume-Capel model there is no multicritical point along the order-disorder transition line. This is in qualitative agreement with mean field prediction but in disagreement with previous approximate renormalization group calculations. We also presented new results for the spin-1 Blume-Capel model.

Reaction-diffusion processes as physical realizations of Hecke algebras

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.

A SYSTEMATIC REVISION OF CAPPARIS SECTION CAPPARIS (CAPPARACEAE)1, 2

Basing on the numerical observations of the eigenspectra of the SU(N) Perk-Schultz model at the special value of the anisotropy q=exp(iπ(N-1)/N), we formulate a set of conjectures concerning the existence of the free-fermion like eigenenergies. We prove analytically a part of these conjectures.

The HeisenbergXXZ Hamiltonian with Dzyaloshinsky-Moriya interactions

Abstract We show that the master equation governing the dynamics of simple diffusion and certain chemical reaction processes in one dimension gives time evolution operators (Hamiltonians) which are realizations of Hecke algebras. In the case of simple diffusion one obtains, after similarity transformations, reducible hermitian representations while in the other cases they are non-hermitian and correspond to supersymmetric quotients of Hecke algebras.

N-species stochastic models with boundaries and quadratic algebras

Abstract A systematic revision of Capparis sect. Capparis, from western and Central Asia, North Africa, and Europe, is presented here. The taxonomy of this section has been approached combining morphological, biogeographical and molecular data when available. Ten species are recognized, including two new species, Capparis atlantica and C. zoharyi. In addition, four new subspecies are presented: Capparis ovata subsp. myrtifolia, C. parviflora subsp. sphaerocarpa, C. sicula subsp. mesopotamica, and C. sicula subsp. sindiana. Lectotypes are designated for C. aegyptia, C. hereroensis, C. mucronifolia, C. elliptica, C. mucronifolia Boiss. subsp. rosanoviana, C. rupestris, C. ovata, C. parviflora, C. spinosa var. canescens, C. sicula subsp. herbacea, and C. sicula subsp. leucophylla. A full taxonomic treatment, keys, and distribution maps of the recognized species are provided. The two new species are illustrated.