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F. C. Alcaraz

Publications and source records attributed to F. C. Alcaraz.

51 records · Page 3Linked to original sources
arXiv1999

New integrable version of the degenerate supersymmetric t-J model

A new integrable version of the degenerate supersymmetric t-J model is proposed. In this formulation instead of restricting single occupancy of electrons at each lattice site we may have up to two electrons at each site. As a requirement of exact integrability the hopping interaction turns out to be correlated with the density of electrons in the neighboring sites. The exact solution of the model is obtained through the coordinate Bethe anzatz.

cond-mat.stat-mech↗
arXiv1999

Exact Solution of a Vertex Model with Unlimited Number of States Per Bond

The exact solution is obtained for the eigenvalues and eigenvectors of the row-to-row transfer matrix of a two-dimensional vertex model with unlimited number of states per bond. This model is a classical counterpart of a quantum spin chain with an unlimited value of spin. This quantum chain is studied using general predictions of conformal field theory. The long-distance behaviour of some ground-state correlation functions is derived from a finite-size analysis of the gapless excitations.

cond-mat.stat-mech↗
arXiv1999

The Critical Behaviour 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 $τ$-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.

cond-mat.stat-mech↗
arXiv1999

Critical and off-critical studies of the Baxter-Wu model with general toroidal boundary conditions

The operator content of the Baxter-Wu model with general toroidal boundary conditions is calculated analytically and numerically. These calculations were done by relating the partition function of the model with the generating function of a site-colouring problem in a hexagonal lattice. Extending the original Bethe-ansatz solution of the related colouring problem we are able to calculate the eigenspectra of both models by solving the associated Bethe-ansatz equations. We have also calculated, by exploring the conformal invariance at the critical point, the mass ratios of the underlying massive theory governing the Baxter-Wu model in the vicinity of its critical point.

cond-mat.stat-mech↗
arXiv1997

New Integrable Generalization of the One-Dimensional t-J Model

A new generalization of the t-J model with a nearest-neigbour hopping is formulated and solved exactly by the Bethe-ansatz method in the thermodymanic limit. The model describes the dymanics of fermions with different spins and with isotropic and anisotropic interactions.

cond-mat.stat-mech↗
arXiv1997

Phase Diagram and Superconducting Properties of an Exactly Solvable Model with Correlated Hopping

The model of strongly correlated electrons with the correlated hopping term and an additional interaction between holes $V$ is solved exactly in one dimension at a special point where the number of hole pairs is conserved. As a function of the interaction $V$ the phase diagram has a rich structure. There exist gapless phases with dominating density-density correlations (metallic) or pair-pair correlations (superconducting) as well insulating and phase-separated phases. The stiffness constant of the conductivity, the effective transport mass, and the compressibility are also exactly calculated in several regions of the phase diagram.

cond-mat.stat-mech↗
arXiv1997

Exact Solution of the Biquadratic Spin-1 t-J Model in One Dimension

A new generalization of the t-J model with a nearest-neigbor hopping is formulated and solved exactly by the Bethe-ansatz method. The model describes the dynamics of spin-S fermions with isotropic or anisotropic interactions. In the case S=1 the magnetic interaction is biquadratic in the spin operators. In contrast to the SU(N) generalization of the t-J model, studied previously in the literature, the present model possesses beyond a massless excitation also a massive one. The physical properties indicate the existence of Cooper-type pairs with finite binding energy.

cond-mat.stat-mech↗
arXiv1997

N-species stochastic models with boundaries and quadratic algebras

Stationary probability distributions for stochastic processes on linear chains with closed or open ends are obtained using the matrix product Ansatz. The matrices are representations of some quadratic algebras. The algebras and the types of representations considered depend on the boundary conditions. In the language of quantum chains we obtain the ground state of N-state quantum chains with free boundary conditions or with non-diagonal boundary terms at one or both ends. In contrast to problems involving the Bethe Ansatz, we do not have a general framework for arbitrary N which when specialized, gives the known results for N=2; in fact, the N=2 and N>2 cases appear to be very different.

cond-mat.stat-mech↗
arXiv1997

Conformal invariance studies of the Baxter-Wu model and a related site-colouring problem

The partition function of the Baxter-Wu model is exactly related to the generating function of a site-colouring problem on a hexagonal lattice. We extend the original Bethe ansatz solution of these models in order to obtain the eigenspectra of their transfer matrices in finite geometries and general toroidal boundary conditions. The operator content of these models are studied by solving numerically the Bethe-ansatz equations and by exploring conformal invariance. Since the eigenspectra are calculated for large lattices, the corrections to finite-size scaling are also calculated.

cond-mat.stat-mech↗
arXiv1996

Critical Behaviour of Mixed Heisenberg Chains

The critical behaviour of anisotropic Heisenberg models with two kinds of antiferromagnetically exchange-coupled centers are studied numerically by using finite-size calculations and conformal invariance. These models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism. Most of our results are centered in the mixed Heisenberg chain where we have at even (odd) sites a spin-S (S') SU(2) operator interacting with a XXZ like interaction (anisotropy $Δ$). Our results indicate universal properties for all these chains. The whole phase, $1>Δ>-1$, where the models change from ferromagnetic $( Δ=1 )$ to ferrimagnetic $(Δ=-1)$ behaviour is critical. Along this phase the critical fluctuations are ruled by a c=1 conformal field theory of Gaussian type. The conformal dimensions and critical exponents, along this phase, are calculated by studying these models with several boundary conditions.

cond-mat.stat-mech↗
arXiv1995

The Critical Behaviour of Potts models with symmetry breaking fields

The $Q$-state Potts model in two dimensions in the presence of external magnetic fields is studied. For general $Q\geq3$ special choices of these magnetic fields produce effective models with smaller $Z(Q')$ symmetry $(Q'< Q)$. The phase diagram of these models and their critical behaviour are explored by conventional finite-size scaling and conformal invariance. The possibility of multicritical behavior, for finite values of the symmetry breaking fields, in the cases where $Q>4$ is also analysed. Our results indicate that for effective models with $Z(Q')$ symmetry $(Q'\leq4)$ the multicritical point occurs at zero field. This last result is also corroborated by Monte Carlo simulations.

cond-mat↗
arXiv1994

Critical and off-critical properties of the $XXZ$ chain in external homogeneous and staggered magnetic fields

The phase diagram of the $XXZ$ chain under the influence of homogeneous and staggered magnetic fields is calculated. The model has a rich phase structure with three types of phases. A fully ferromagnetic phase, an antiferromagnetic phase and a massless phase with partial ferromagnetic and antiferromagnetic order. This massless phase has its critical fluctuations governed by a conformal field theory with central charge $c=1$. When the $σ^{z}$-anisotropy $Δ$ is zero the model is exactly integrable through a Jordan-Wigner fermionization and our results are analytic. For $Δ\neq 0 $ our analysis are done numerically using lattice sizes up to $M=20$. Our results shows that for $-1 \geq Δ\geq \frac{\sqrt{2}}{2}$ the staggered magnetic field perturbation is relevant and for $1 \leq Δ\leq \frac{\sqrt{2}}{2}$ it is irrelevant. In the region of relevant perturbations we show that the massive continuum field theory associated to the model has the same mass spectrum as the sine-Gordon model.

cond-mat↗
arXiv1994

Finite Chains with Quantum Affine Symmetries

We consider an extension of the (t-U) Hubbard model taking into account new interactions between the numbers of up and down electrons. We confine ourselves to a one-dimensional open chain with L sites (4^L states) and derive the effective Hamiltonian in the strong repulsion (large U) regime. This Hamiltonian acts on 3^L states. We show that the spectrum of the latter Hamiltonian (not the degeneracies) coincides with the spectrum of the anisotropic Heisenberg chain (XXZ model) in the presence of a Z field (2^L states). The wave functions of the 3^L-state system are obtained explicitly from those of the 2^L-state system, and the degeneracies can be understood in terms of irreducible representations of U_q(\hat{sl(2)}).

hep-th↗
arXiv1993

Reaction-Diffusion Processes as Physical Realizations of Hecke Algebras

We show that the master equation governing the dynamics of simple diffusion and certain chemical reaction processes in one dimension give 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.

hep-th↗