Publications (91)139.68 Total impact
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ABSTRACT: We obtained the exact solution of a probabilistic cellular automaton related to the diagonaltodiagonal transfer matrix of the sixvertex model on a square lattice. The model describes the flow of ants (or particles), traveling on a onedimensional lattice whose sites are small craters containing sleeping or awake ants (two kinds of particles). We found the Bethe ansatz equations and the spectral gap for the timeevolution operator of the cellular automaton. From the spectral gap we show that in the asymmetric case it belongs to the KardarParisiZhang (KPZ) universality class, exhibiting a dynamical critical exponent value $z=\frac{3}{2}$. This result is also obtained from a direct Monte Carlo simulation, by evaluating the latticesize dependence of the decay time to the stationary state.  [Show abstract] [Hide abstract]
ABSTRACT: We study the R\'enyi mutual information $\tilde{I}_n$ of the ground state of different critical quantum chains. The R\'enyi mutual information definition that we use is based on the well established concept of the R\'enyi divergence. We calculate this quantity numerically for several distinct quantum chains having either discrete $Z(Q)$ symmetries (Qstate Potts model with $Q=2,3,4$ and $Z(Q)$ parafermionic models with $Q=5,6,7,8$ and also AshkinTeller model with different anisotropies) or the $U(1)$ continuous symmetries(KleinGordon field theory, XXZ and spin1 FateevZamolodchikov quantum chains with different anisotropies). For the spin chains these calculations were done by expressing the groundstate wavefunctions in two special basis. Our results indicate some general behavior for particular ranges of values of the parameter $n$ that defines $\tilde{I}_n$. For a system, with total size $L$ and subsystem sizes $\ell$ and $L\ell$, the$\tilde{I}_n$ has a logarithmic leading behavior given by $\frac{\tilde{c}_n}{4}\log(\frac{L}{\pi}\sin(\frac{\pi \ell}{L}))$ where the coefficient $\tilde{c}_n$ is linearly dependent on the central charge $c$ of the underlying conformal field theory (CFT) describing the system's critical properties.  [Show abstract] [Hide abstract]
ABSTRACT: A lattice model of critical dense polymers $O(0)$ is considered for the finite cylinder geometry. Due to the presence of noncontractible 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 noncontractible 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.  [Show abstract] [Hide abstract]
ABSTRACT: We study the Shannon and R\'enyi mutual information (MI) in the ground state (GS) of 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 finitesize 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[\frac{L}{$\pi${}}sin(\frac{$\pi${}$\ell${}}{L})]$, when the groundstate 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 ${b}_{n}ln[\frac{L}{$\pi${}}sin(\frac{$\pi${}$\ell${}}{L})]$ 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 AshkinTeller 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. 
Article: Universal behavior of the Shannon and R\'enyi mutual information of quantum critical chains
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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 finitesize 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 $\frac{c}{4}\frac{n}{n1}\ln\Big{(}\frac{L}{\pi}\sin(\frac{\pi \ell}{L})\Big{)}$, when the groundstate 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 AshkinTeller 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 $8$. 
Article: Universal behavior of the Shannon and R\'enyi mutual information of quantum critical chains
[Show abstract] [Hide abstract]
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 finitesize 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 $\frac{c}{4}\frac{n}{n1}\ln\Big{(}\frac{L}{\pi}\sin(\frac{\pi \ell}{L})\Big{)}$, when the groundstate 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 AshkinTeller 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 $8$.  [Show abstract] [Hide abstract]
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 finitesize behavior yields the conformal anomaly $c$ of the underlying conformal field theory governing the long distance physics of the quantum chain. We studied analytically a chain of coupled harmonic oscillators and numerically the Qstate Potts models ($Q = 2$; 3 and 4), the XXZ quantum chain and the spin1 FateevZamolodchikov model. The Shannon mutual information is a quantity easily computed, and our results indicate that for relatively small lattice sizes its finitesize behavior already detects the universality class of quantum critical behavior.  [Show abstract] [Hide abstract]
ABSTRACT: We study the entanglement entropies in onedimensional open critical systems, whose effective description is given by a conformal field theory with boundaries. We show that for purestate systems formed by the ground state or by the excited states associated to primary fields, the entanglement entropies have a finitesize 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 $c=1$.  [Show abstract] [Hide abstract]
ABSTRACT: We consider an extension of the tU Hubbard model taking into account new interactions between the numbers of up and down electrons. We confine ourselves to a onedimensional 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 3Lstate system are obtained explicitly from those of the 2Lstate system, and the degeneracies can be understood in terms of irreducible representations of .  [Show abstract] [Hide abstract]
ABSTRACT: Using the density matrix renormalization group, we calculated the finitesize 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 spin1/2 XXZ and spin1 FateevZamolodchikov models, as well models with discrete symmetries such as the Ising, the BlumeCapel and the threestate 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 longdistance 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 finitesize correction of the $\alpha$Renyi entropies. We conjecture that the exponent of the leading finitesize 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.  [Show abstract] [Hide abstract]
ABSTRACT: Finitesize 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 spin1 BlumeCapel 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.  [Show abstract] [Hide abstract]
ABSTRACT: Using the density matrix renormalization group, we investigate the Rényi entropy of the anisotropic spins Heisenberg chains in a zmagnetic field. We considered the halfoddinteger spins chains, with s=1/2, 3/2, and 5/2, and periodic and open boundary conditions. In the case of the spin1/2 chain we were able to obtain accurate estimates of the new parity exponents pα(p) and pα(o) that gives the powerlaw decay of the oscillations of the αRényi 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 spin3/2 chain are not so accurate, they are consistent with the theoretical predictions.  [Show abstract] [Hide abstract]
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 nonnegative numbers and therefore can be interpreted as probabilities of configurations. Such ground states of Hermitian and nonHermitian 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.  [Show abstract] [Hide abstract]
ABSTRACT: We present four estimators of the entanglement (or interdepency) of groundstates in which the coefficients are all real nonnegative and therefore can be interpreted as probabilities of configurations. Such groundstates of hermitian and nonhermitian 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 nonconformal 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  [Show abstract] [Hide abstract]
ABSTRACT: In onecomponent 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 twocomponent quadratic Abelian algebras. We show that Abelian sandpile models with two conservation laws have only trivial avalanches.  [Show abstract] [Hide abstract]
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 spin1/2 XXZ chain with an arbitrary length $L$ for both periodic and twisted boundary conditions.  [Show abstract] [Hide abstract]
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.  [Show abstract] [Hide abstract]
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 L1L7 and F C Alcaraz and M J Lazo 2004 J. Phys. A: Math. Gen. 37 414982).  [Show abstract] [Hide abstract]
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).  [Show abstract] [Hide abstract]
ABSTRACT: We discuss entanglement in the spin1/2 anisotropic ferromagnetic Heisenberg chain in the presence of a boundary magnetic field generating domain walls. By increasing the magnetic field, the model undergoes a firstorder quantum phase transition from a ferromagnetic to a kinktype 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 nonvanishing 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 kinktype phase. Comment: v3: 7 pages, including 4 figures and 1 table. Published version. v2: One section (V) added and references updated
Publication Stats
2k  Citations  
139.68  Total Impact Points  
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Institutions

20022015

University of São Paulo
 Institute of Physics São Carlos (IFSC)
San Paulo, São Paulo, Brazil


19812002

Universidade Federal de São Carlos
 Departamento de Física (DF)
São Carlos do Pinhal, São Paulo, Brazil


1998

Australian National University
 Department of Mathematics
Canberra, Australian Capital Territory, Australia


19921998

University of California, Santa Barbara
 Kavli Institute for Theoretical Physics
Santa Barbara, CA, United States
