arXiv subjects

F. C. Alcaraz

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

At least 19 recordsLinked to original sources

arXiv2018

Equipartition of the Entanglement Entropy

The entanglement in a quantum system that possess an internal symmetry, characterized by the Sz-magnetization or U(1)-charge, is distributed among different sectors. The aim of this letter is to gain a deeper understanding of the contribution to the entanglement entropy in each of those sectors for the ground state of conformal invariant critical one dimensional systems. We find surprisingly that the entanglement entropy is equally distributed among the different magnetization sectors. Its value is given by the standard area law violating logarithmic term, that depends on the central charge c, minus a double logarithmic correction related to the zero temperature susceptibility. This result provides a new method to estimate simultaneously the central charge c and the critical exponents of U(1)-symmetric quantum chains. The method is numerically simple and gives precise results for the spin-1/2 quantum XXZ chain. We also compute the probability distribution of the magnetization in contiguous sublattices.

cond-mat.stat-mech↗

arXiv2018

Critical phases in the raise and peel model

The raise and peel model (RPM) is a nonlocal stochastic model describing the space and time fluctuations of an evolving one dimensional interface. Its relevant parameter $u$ is the ratio between the rates of local adsorption and nonlocal desorption processes (avalanches) processes. The model at $u=1$ give us the first example of a conformally invariant stochastic model. For small values $u u_0$ it is critical. By calculating the structure function of the height profiles in the reciprocal space we confirm with good precision that indeed $u_0=1$. We establish that at the conformal invariant point $u=1$ the RPM has a roughness transition with dynamical and roughness critical exponents $z=1$ and $α=0$, respectively. For $u>1$ the model is critical with an $u$-dependent dynamical critical exponent $z(u)$ that tends towards zero as $u\to \infty$. However at $1/u=0$ the RPM is exactly mapped into the totally asymmetric exclusion problem (TASEP). This last model is known to be noncritical (critical) for open (periodic) boundary conditions. Our studies indicate that the RPM as $u \to \infty$, due to its nonlocal dynamics processes, has the same large-distance physics no matter what boundary condition we chose. For $u>1$, our analysis show that differently from previous predictions, the region is composed by two distinct critical phases. For $u\leq u < u_c\approx 40$ the height profiles are rough ($α= α(u) >0$), and for $u>u_c$ the height profiles are flat at large distances ($α= α(u) <0$). We also observed that in both critical phases ($u>1$) the RPM at short length scales, has an effective behavior in the Kardar-Parisi-Zhang (KPZ) critical universality class, that is not the true behavior of the system at large length scales.

cond-mat.stat-mech↗

arXiv2017

Quasi-stationary states in nonlocal stochastic growth models with infinitely many absorbing states

We study a two parameter ($u,p$) extension of the conformally invariant raise and peel model. The model also represents a nonlocal and biased-asymmetric exclusion process with local and nonlocal jumps of excluded volume particles in the lattice. The model exhibits an unusual and interesting critical phase where, in the bulk limit, there are an infinite number of absorbing states. In spite of these absorbing states the system stays, during a time that increases exponentially with the lattice size, in a critical quasi-stationary state. In this critical phase the critical exponents depend only on one of the parameters defining the model ($u$). The endpoint of this critical phase belongs to a distinct universality class, where the system changes from an active to an inactive frozen state. This new behavior we believe to be due to the appearance of Jordan cells in the Hamiltonian describing the time evolution. The dimensions of these cells increases with the lattice size. In a special case ($u=0$) where the model has no adsorptions we are able to calculate analytically the time evolution of some of the observables. A polynomial time dependence is obtained due to the Jordan cells structure of the Hamiltonian.

cond-mat.stat-mech↗

arXiv2016

Universal behavior of the Shannon mutual information in non-integrable self-dual quantum chains

An existing conjecture states that the Shannon mutual information contained in the ground state wavefunction of conformally invariant quantum chains, on periodic lattices, has a leading finite-size scaling behavior that, similarly as the von Neumann entanglement entropy, depends on the value of the central charge of the underlying conformal field theory describing the physical properties. This conjecture applies whenever the ground state wavefunction is expressed in some special basis (conformal basis). Its formulation comes mainly from numerical evidences on exactly integrable quantum chains. In this paper the above conjecture was tested for several general non-integrable quantum chains. We introduce new families of self-dual $Z(Q)$ symmetric quantum chains ($Q=2,3,\ldots$). These quantum chains contain nearest neighbour as well next-nearest neighbour interactions (coupling constant $p$). In the cases $Q=2$ and $Q=3$ they are extensions of the standard quantum Ising and 3-state Potts chains, respectively. For $Q=4$ and $Q\geq 5$ they are extensions of the Ashkin-Teller and $Z(Q)$ parafermionic quantum chains. Our studies indicate that these models are interesting on their own. They are critical, conformally invariant, and share the same universality class in a continuous critical line. Moreover, our numerical analysis for $Q=2-8$ indicate that the Shannon mutual information exhibits the conjectured behaviour irrespective if the conformally invariant quantum chain is exactly integrable or not. For completeness we also calculated, for these new families of quantum chains, the two existing generalizations of the Shannon mutual information, which are based on the Rényi entropy and on the Rényi divergence.

cond-mat.stat-mech↗

arXiv2015

The spectral gap and the dynamical critical exponent of an exact solvable probabilistic cellular automaton

We obtained the exact solution of a probabilistic cellular automaton related to the diagonal-to-diagonal transfer matrix of the six-vertex model on a square lattice. The model describes the flow of ants (or particles), traveling on a one-dimensional 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 time-evolution operator of the cellular automaton. From the spectral gap we show that in the asymmetric case it belongs to the Kardar-Parisi-Zhang (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 lattice-size dependence of the decay time to the stationary state.

cond-mat.stat-mech↗

arXiv2015

Generalized mutual informations of quantum critical chains

We study the Rényi mutual information $\tilde{I}_n$ of the ground state of different critical quantum chains. The Rényi mutual information definition that we use is based on the well established concept of the Rényi divergence. We calculate this quantity numerically for several distinct quantum chains having either discrete $Z(Q)$ symmetries (Q-state Potts model with $Q=2,3,4$ and $Z(Q)$ parafermionic models with $Q=5,6,7,8$ and also Ashkin-Teller model with different anisotropies) or the $U(1)$ continuous symmetries(Klein-Gordon field theory, XXZ and spin-1 Fateev-Zamolodchikov quantum chains with different anisotropies). For the spin chains these calculations were done by expressing the ground-state 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 $\frac{\tilde{c}_n}{4}\log(\frac{L}π\sin(\frac{π\ell}{L}))$ 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.

cond-mat.stat-mech↗

arXiv2015

Non-contractible loops in the dense O(n) loop model on the cylinder

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 $ξ$, 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 $ρ$ 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 $ρ$ for any $O(n)$ model and an arbitrary fugacity.

cond-mat.stat-mech↗

arXiv2014

Universal behavior of the Shannon and Rényi mutual information of quantum critical chains

We study the Shannon and Rényi 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 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 $\frac{c}{4}\frac{n}{n-1}\ln\Big{(}\frac{L}π\sin(\frac{π\ell}{L})\Big{)}$, when the ground-state wavefunction 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 $b_n\ln\Big{(}\frac{L}π\sin(\frac{π\ell}{L})\Big{)}$ 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 $8$.

cond-mat.stat-mech↗

arXiv2013

Entanglement Entropies in Conformal Systems with Boundaries

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 $c=1$.

cond-mat.stat-mech↗

arXiv2013

Universal behavior of the Shannon mutual information of critical quantum chains

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 studied 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.

cond-mat.stat-mech↗

arXiv2012

Finite-size corrections of the Entanglement Entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement $α$-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 $α$, 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 $α$-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the $α$-Renyi entropies is $p_α=2X_ε/α$ for $α>1$ and $p_{1}=ν$, where $X_ε$ is the dimensions of the energy operator of the model and $ν=2$ for all the models.

cond-mat.stat-mech↗

arXiv2011

Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law

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.

cond-mat.stat-mech↗

arXiv2011

Renyi Entropy and Parity Oscillations of the Anisotropic Spin-s Heisenberg Chains in a Magnetic Field

Using the density matrix renormalization group, we investigate the Renyi 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 $p_α^{(p)}$ and $p_α^{(o)}$ that gives the power-law decay of the oscillations of the $α-$Renyi 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 non-zero 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 $p_α^{(p)}$ and $p_α^{(o)}$ become a challenge. Although our estimates of the new universal exponents $p_α^{(p)}$ and $p_α^{(o)}$ for the spin-3/2 chain are not so accurate, they are consistent with the theoretical predictions.

cond-mat.stat-mech↗

arXiv2010

Shared Information in Stationary States at Criticality

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.

cond-mat.stat-mech↗

arXiv2009

Entanglement in Far From Equilibrium Stationary States

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.

cond-mat.stat-mech↗

arXiv2009

Two-component abelian sandpile models

In one-component abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multi-component models. The condition of associativity of the underlying abelian algebras impose 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.

cond-mat.stat-mech↗

arXiv2008

Finite Size Corrections to Entanglement in Quantum Critical Systems

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.

quant-ph↗

arXiv2007

The pair annihilation reaction D + D --> 0 in disordered media and conformal invariance

The raise and peel model describes the 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 defect 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 conformal invariant quantum chain.

cond-mat.stat-mech↗