F. C. Alcaraz

University of São Paulo, San Paulo, São Paulo, Brazil

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Publications (100)172.85 Total impact

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    ABSTRACT: A lattice model of critical dense polymers $O(0)$ is considered for the finite cylinder geometry. Due to the presence of non-contractible loops with a fixed fugacity $\xi$, the model is a generalization of the critical dense polymers solved by Pearce, Rasmussen and Villani. We found the free energy for any height $N$ and circumference $L$ of the cylinder. The density $\rho$ of non-contractible loops is found for $N \rightarrow \infty$ and large $L$. The results are compared with those obtained for the anisotropic quantum chain with twisted boundary conditions. Using the latter method we obtained $\rho$ for any $O(n)$ model and an arbitrary fugacity.
    09/2014;
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    F. C. Alcaraz, M. A. Rajabpour
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    ABSTRACT: We study the Shannon and R\'enyi mutual information (MI) in different critical quantum spin chains. Despite the apparent basis dependence of these quantities we show the existence of some particular basis (we will call them conformal basis) whose finite-size scaling function is related to the central charge $c$ of the underlying conformal field theory of the model. In particular, we verified that for large index $n$, the MI of a subsystem of size $\ell$ in a periodic chain with $L$ sites behaves as $\frac{c}{4}\frac{n}{n-1}\ln\Big{(}\frac{L}{\pi}\sin(\frac{\pi \ell}{L})\Big{)}$, when the ground-state wave function is expressed in these special conformal basis. This is in agreement with recent predictions. For generic local basis we will show that, although in some cases $b_n\ln\Big{(}\frac{L}{\pi}\sin(\frac{\pi \ell}{L})\Big{)}$ is a good fit to our numerical data, in general there is no direct relation between $b_n$ and the central charge of the system. We will support our findings with detailed numerical calculations for the transverse field Ising model, $Q=3,4$ quantum Potts chain, quantum Ashkin-Teller chain and the XXZ quantum chain. We will also present some additional results of the Shannon mutual information ($n=1$), for the parafermionic $Z(Q)$ quantum chains with $Q=5,6,7$ and $8$.
    05/2014;
  • F. C. Alcaraz, M. A. Rajabpour
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    ABSTRACT: We study the Shannon and R\'enyi mutual information (MI) in different critical quantum spin chains. Despite the apparent basis dependence of these quantities we show the existence of some particular basis (we will call them conformal basis) whose finite-size scaling function is related to the central charge $c$ of the underlying conformal field theory of the model. In particular, we verified that for large index $n$, the MI of a subsystem of size $\ell$ in a periodic chain with $L$ sites behaves as $\frac{c}{4}\frac{n}{n-1}\ln\Big{(}\frac{L}{\pi}\sin(\frac{\pi \ell}{L})\Big{)}$, when the ground-state wave function is expressed in these special conformal basis. This is in agreement with recent predictions. For generic local basis we will show that, although in some cases $b_n\ln\Big{(}\frac{L}{\pi}\sin(\frac{\pi \ell}{L})\Big{)}$ is a good fit to our numerical data, in general there is no direct relation between $b_n$ and the central charge of the system. We will support our findings with detailed numerical calculations for the transverse field Ising model, $Q=3,4$ quantum Potts chain, quantum Ashkin-Teller chain and the XXZ quantum chain. We will also present some additional results of the Shannon mutual information ($n=1$), for the parafermionic $Z(Q)$ quantum chains with $Q=5,6,7$ and $8$.
    04/2014;
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    F C Alcaraz, M A Rajabpour
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    ABSTRACT: We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Our results indicate a universal leading behavior for large subsystem sizes. Moreover, as happens with the entanglement entropy, its finite-size behavior yields the conformal anomaly c of the underlying conformal field theory governing the long-distance physics of the quantum chain. We study analytically a chain of coupled harmonic oscillators and numerically the Q-state Potts models (Q=2, 3, and 4), the XXZ quantum chain, and the spin-1 Fateev-Zamolodchikov model. The Shannon mutual information is a quantity easily computed, and our results indicate that for relatively small lattice sizes, its finite-size behavior already detects the universality class of quantum critical behavior.
    Physical Review Letters 07/2013; 111(1):017201. · 7.73 Impact Factor
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    L. Taddia, J. C. Xavier, F. C. Alcaraz, G. Sierra
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    ABSTRACT: We study the entanglement entropies in one-dimensional open critical systems, whose effective description is given by a conformal field theory with boundaries. We show that for pure-state systems formed by the ground state or by the excited states associated to primary fields, the entanglement entropies have a finite-size behavior that depends on the correlation of the underlying field theory. The analytical results are checked numerically, finding excellent agreement for the quantum chains ruled by the theories with central charge $c=1/2$ and $c=1$.
    Physical review. B, Condensed matter 02/2013; 88(7). · 3.77 Impact Factor
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    ABSTRACT: 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 (4L states) and derive the effective Hamiltonian in the strong repulsion (large U) regime. This Hamiltonian acts on 3L states. We show that the spectrum of the latter Hamiltonian (not the degeneracies) coincides with the spectrum of the anisotropic Heisenberg chain (XX Z model) in the presence of a Z field (2L states). The wave functions of the 3L-state system are obtained explicitly from those of the 2L-state system, and the degeneracies can be understood in terms of irreducible representations of .
    International Journal of Modern Physics A 01/2012; 09(19). · 1.13 Impact Factor
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    J. C. Xavier, F. C. Alcaraz
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    ABSTRACT: Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement $\alpha$-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry like the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well models with discrete symmetries such as the Ising, the Blume-Capel and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, that depend on the value of $\alpha$, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the $\alpha$-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the $\alpha$-Renyi entropies is $p_{\alpha}=2X_{\epsilon}/\alpha$ for $\alpha>1$ and $p_{1}=\nu$, where $X_{\epsilon}$ is the dimensions of the energy operator of the model and $\nu=2$ for all the models.
    Physical review. B, Condensed matter 11/2011; 85(2). · 3.77 Impact Factor
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    J. C. Xavier, F. C. Alcaraz
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    ABSTRACT: Finite-size scaling analysis turns out to be a powerful tool to calculate the phase diagram as well as the critical properties of two dimensional classical statistical mechanics models and quantum Hamiltonians in one dimension. The most used method to locate quantum critical points is the so called crossing method, where the estimates are obtained by comparing the mass gaps of two distinct lattice sizes. The success of this method is due to its simplicity and the ability to provide accurate results even considering relatively small lattice sizes. In this paper, we introduce an estimator that locates quantum critical points by exploring the known distinct behavior of the entanglement entropy in critical and non critical systems. As a benchmark test, we use this new estimator to locate the critical point of the quantum Ising chain and the critical line of the spin-1 Blume-Capel quantum chain. The tricritical point of this last model is also obtained. Comparison with the standard crossing method is also presented. The method we propose is simple to implement in practice, particularly in density matrix renormalization group calculations, and provides us, like the crossing method, amazingly accurate results for quite small lattice sizes. Our applications show that the proposed method has several advantages, as compared with the standard crossing method, and we believe it will become popular in future numerical studies.
    Physical review. B, Condensed matter 06/2011; 84. · 3.77 Impact Factor
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    J. C. Xavier, F. C. Alcaraz
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    ABSTRACT: Using the density matrix renormalization group, we investigate the Rényi entropy of the anisotropic spin-s Heisenberg chains in a z-magnetic field. We considered the half-odd-integer spin-s chains, with s=1/2, 3/2, and 5/2, and periodic and open boundary conditions. In the case of the spin-1/2 chain we were able to obtain accurate estimates of the new parity exponents pα(p) and pα(o) that gives the power-law decay of the oscillations of the α-Rényi entropy for periodic and open boundary conditions, respectively. We confirm the relations of these exponents with the Luttinger parameter K, as proposed by Calabrese et al. [ Phys. Rev. Lett. 104 095701 (2010)]. Moreover, the predicted periodicity of the oscillating term was also observed for some nonzero values of the magnetization m. We show that for s>1/2 the amplitudes of the oscillations are quite small and get accurate estimates of pα(p) and pα(o) become a challenge. Although our estimates of the new universal exponents pα(p) and pα(o) for the spin-3/2 chain are not so accurate, they are consistent with the theoretical predictions.
    Physical review. B, Condensed matter 03/2011; 83(21). · 3.77 Impact Factor
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    F. C. Alcaraz, V. Rittenberg
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    ABSTRACT: We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the shared information between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behavior of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance. Comment: 25 pages, 12 figures
    Journal of Statistical Mechanics Theory and Experiment 12/2009; · 1.87 Impact Factor
  • F C Alcaraz, V Rittenberg, G Sierra
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    ABSTRACT: We present four estimators of the shared information (or interdepency) in ground states given that the coefficients appearing in the wave function are all real non-negative numbers and therefore can be interpreted as probabilities of configurations. Such ground states of Hermitian and non-Hermitian Hamiltonians can be given, for example, by superpositions of valence bond states which can describe equilibrium but also stationary states of stochastic models. We consider in detail the last case, the system being a classical not a quantum one. Using analytical and numerical methods we compare the values of the estimators in the directed polymer and the raise and peel models which have massive, conformal invariant and nonconformal invariant massless phases. We show that like in the case of the quantum problem, the estimators verify the area law with logarithmic corrections when phase transitions take place.
    Physical Review E 09/2009; 80(3 Pt 1):030102. · 2.31 Impact Factor
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    F. C. Alcaraz, V. Rittenberg, G. Sierra
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    ABSTRACT: We present four estimators of the entanglement (or interdepency) of ground-states in which the coefficients are all real nonnegative and therefore can be interpreted as probabilities of configurations. Such ground-states of hermitian and non-hermitian Hamiltonians can be given, for example, by superpositions of valence bond states which can describe equilibrium but also stationary states of stochastic models. We consider in detail the last case. Using analytical and numerical methods we compare the values of the estimators in the directed polymer and the raise and peel models which have massive, conformal invariant and non-conformal invariant massless phases. We show that like in the case of the quantum problem, the estimators verify the area law and can therefore be used to signal phase transitions in stationary states. Comment: 4 pages 3figures
    05/2009;
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    F C Alcaraz, P Pyatov, V Rittenberg
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    ABSTRACT: In one-component Abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multicomponent models. The condition of associativity of the underlying Abelian algebras imposes nonlinear relations among the toppling probabilities. These relations are derived for the case of two-component quadratic Abelian algebras. We show that Abelian sandpile models with two conservation laws have only trivial avalanches.
    Physical Review E 05/2009; 79(4 Pt 1):042102. · 2.31 Impact Factor
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    F. C. Alcaraz, M. S. Sarandy
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    ABSTRACT: We analyze the finite size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system $L \to \infty$) exhibit a unique pattern of entanglement, which differ only at leading order $(1/L)^2$. In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary length $L$ for both periodic and twisted boundary conditions.
    Physical Review A 09/2008; 78:032319. · 3.04 Impact Factor
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    F C Alcaraz, V Rittenberg
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    ABSTRACT: The raise and peel model is a stochastic model of a fluctuating interface separating a substrate covered with clusters of matter of different sizes and a rarefied gas of tiles. The stationary state is obtained when adsorption compensates the desorption of tiles. This model is generalized to an interface with defects (D) . The defects are either adjacent or separated by a cluster. If a tile hits the end of a cluster with a defect nearby, the defect hops at the other end of the cluster, changing its shape. If a tile hits two adjacent defects, the defects annihilate and are replaced by a small cluster. There are no defects in the stationary state. This model can be seen as describing the reaction D+D-->0 , in which the particles (defects) D hop at long distances, changing the medium, and annihilate. Between the hops the medium also changes (tiles hit clusters, changing their shapes). Several properties of this model are presented and some exact results are obtained using the connection of our model with a conformally invariant quantum chain.
    Physical Review E 05/2007; 75(5 Pt 1):051110. · 2.31 Impact Factor
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    F. C. Alcaraz, M. J. Lazo
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    ABSTRACT: We present a general formulation of the matrix product ansatz for exactly integrable chains on periodic lattices. This new formulation extends the matrix product ansatz present in our previous articles (F C Alcaraz and M J Lazo 2004 J. Phys. A: Math. Gen. 37 L1-L7 and F C Alcaraz and M J Lazo 2004 J. Phys. A: Math. Gen. 37 4149-82).
    Journal of Physics A General Physics 01/2006; 391:11335-11337.
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    F. C. Alcaraz, A. Saguia, M. S. Sarandy
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    ABSTRACT: We discuss entanglement in the spin-1/2 anisotropic ferromagnetic Heisenberg chain in the presence of a boundary magnetic field generating domain walls. By increasing the magnetic field, the model undergoes a first-order quantum phase transition from a ferromagnetic to a kink-type phase, which is associated to a jump in the content of entanglement available in the system. Above the critical point, pairwise entanglement is shown to be non-vanishing and independent of the boundary magnetic field for large chains. Based on this result, we provide an analytical expression for the entanglement between arbitrary spins. Moreover the effects of the quantum domains on the gapless region and for antiferromagnetic anisotropy are numerically analysed. Finally multiparticle entanglement properties are considered, from which we establish a characterization of the critical anisotropy separating the gapless regime from the kink-type phase. Comment: v3: 7 pages, including 4 figures and 1 table. Published version. v2: One section (V) added and references updated
    Physical Review A 09/2004; 70:032333. · 3.04 Impact Factor
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    F. C. Alcaraz, M. J. Lazo
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    ABSTRACT: Most of the exact solutions of quantum one-dimensional Hamiltonians are obtained thanks to the success of the Bethe ansatz on its several formulations. According to this ansatz the amplitudes of the eigenfunctions of the Hamiltonian are given by a sum of permutations of appropriate plane waves. In this paper, alternatively, we present a matrix product ansatz that asserts that those amplitudes are given in terms of a matrix product. The eigenvalue equation for the Hamiltonian define the algebraic properties of the matrices defining the amplitudes. The existence of a consistent algebra imply the exact integrability of the model. The matrix product ansatz we propose allow an unified and simple formulation of several exact integrable Hamiltonians. In order to introduce and illustrate this ansatz we present the exact solutions of several quantum chains with one and two global conservation laws and periodic boundaries such as the XXZ chain, spin-1 Fateev-Zamolodchikov model, Izergin-Korepin model, Sutherland model, t-J model, Hubbard model, etc. Formulation of the matrix product ansatz for quantum chains with open ends is also possible. As an illustration we present the exact solution of an extended XXZ chain with $z$-magnetic fields at the surface and arbitrary hard-core exclusion among the spins.
    Journal of Physics A General Physics 01/2004;
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    F. C. Alcaraz, Yu. G. Stroganov
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    ABSTRACT: We present a new conjecture for the SUq(N) Perk–Schultz models. This conjecture extends a conjecture presented in our article (Alcaraz F C and Stroganov Yu G J. Phys. A: Math. Gen.35 6767–87).
    Journal of Physics A General Physics 01/2004; 37(48):11725-11727.
  • F. C. Alcaraz, Yu. G. Stroganov
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    ABSTRACT: 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.
    International Journal of Modern Physics A 01/2004; 19(supp02):1-15. · 1.13 Impact Factor

Publication Stats

1k Citations
172.85 Total Impact Points

Institutions

  • 2002–2014
    • University of São Paulo
      • Institute of Physics São Carlos (IFSC)
      San Paulo, São Paulo, Brazil
  • 1986–2002
    • Universidade Federal de São Carlos
      • Departamento de Física (DF)
      São Carlos, Estado de Sao Paulo, Brazil
  • 1986–1998
    • Australian National University
      • Department of Mathematics
      Canberra, Australian Capital Territory, Australia
  • 1982–1998
    • University of California, Santa Barbara
      • Kavli Institute for Theoretical Physics
      Santa Barbara, CA, United States
  • 1989
    • University of Bonn
      • Physics Institute
      Bonn, North Rhine-Westphalia, Germany
  • 1985
    • University of Michigan
      • Department of Physics
      Ann Arbor, MI, United States