Showing papers in "Journal of Physics A in 2009"
TL;DR: In this paper, a conformal field theory approach to entanglement entropy in 1+1 dimensions is presented, and the authors show how to apply these methods to the calculation of the entropy of a single interval and the generalization to different situations such as finite size, systems with boundaries and the case of several disjoint intervals.
Abstract: We review the conformal field theory approach to entanglement entropy in 1+1 dimensions. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite size, systems with boundaries and the case of several disjoint intervals. We discuss the behaviour away from the critical point and the spectrum of the reduced density matrix. Quantum quenches, as paradigms of non-equilibrium situations, are also considered.
1,267 citations
TL;DR: In this article, four lectures on holography and the AdS/CFT correspondence applied to condensed matter systems were presented, the first lecture introduces the concept of a quantum phase transition and the second lecture discusses linear response theory and Ward identities.
Abstract: Four lectures on holography and the AdS/CFT correspondence applied to condensed matter systems 1 . The first lecture introduces the concept of a quantum phase transition. The second lecture discusses linear response theory and Ward identities. The third lecture presents transport coefficients derived from AdS/CFT that should be applicable in the quantum critical region associated with a quantum phase transition. The fourth lecture builds in the physics of a superconducting or superfluid phase transition to the simple holographic model of the third lecture.
1,006 citations
TL;DR: In this article, the authors review recent progress on the holographic understanding of the entanglement entropy in the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence.
Abstract: In this paper, we review recent progress on the holographic understanding of the entanglement entropy in the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence. In general, the AdS/CFT relates physical observables in strongly coupled quantum many-body systems to certain classical quantities in gravity plus matter theories. In the case of our holographic entanglement entropy, its gravity dual turns out to be purely geometric, i.e. the area of minimal area surfaces in AdS spaces. One interesting application is to study various phase transitions by regarding the entanglement entropy as order parameters. Indeed we will see that our holographic calculations nicely reproduce the confinement/deconfinement transition. Our results can also be applied to understanding the microscopic origins of black hole entropy.
984 citations
TL;DR: In this article, it was shown that a nearby Hamiltonian exists for which the transition amplitudes between any eigenstates of the original Hamiltonian are exactly zero for all values of slowness.
Abstract: For a general quantum system driven by a slowly time-dependent Hamiltonian, transitions between instantaneous eigenstates are exponentially weak. But a nearby Hamiltonian exists for which the transition amplitudes between any eigenstates of the original Hamiltonian are exactly zero for all values of slowness. The general theory is illustrated by spins driven by changing magnetic fields, and implies that any spin expectation history, including those where the spin never precesses, can be generated by infinitely many driving fields, here displayed explicitly. Asymptotically, the absence of transitions is explained by continuation to complex time, where the complex degeneracies in the transitionless driving fields have a nongeneric structure for which there is no Stokes phenomenon; this is analogous to the explanation of reflectionless potentials.
827 citations
TL;DR: In this paper, the Feshbach projection operator is used to represent the interior of the localized part of an open quantum system in the set of eigenfunctions of the Hamiltonian Heff.
Abstract: The Hamiltonian Heff of an open quantum system consists formally of a first-order interaction term describing the closed (isolated) system with discrete states and a second-order term caused by the interaction of the discrete states via the common continuum of scattering states. Under certain conditions, the last term may be dominant. Due to this term, Heff is non-Hermitian. Using the Feshbach projection operator formalism, the solution ΨEc of the Schrodinger equation in the whole function space (with discrete as well as scattering states, and the Hermitian Hamilton operator H) can be represented in the interior of the localized part of the system in the set of eigenfunctions λ of Heff. Hence, the characteristics of the eigenvalues and eigenfunctions of the non-Hermitian operator Heff are contained in observable quantities. Controlling the characteristics by means of external parameters, quantum systems can be manipulated. This holds, in particular, for small quantum systems coupled to a small number of channels. The paper consists of three parts. In the first part, the eigenvalues and eigenfunctions of non-Hermitian operators are considered. Most important are the true and avoided crossings of the eigenvalue trajectories. In approaching them, the phases of the λ lose their rigidity and the values of observables may be enhanced. Here the second-order term of Heff determines decisively the dynamics of the system. The time evolution operator is related to the non-Hermiticity of Heff. In the second part of the paper, the solution ΨEc and the S matrix are derived by using the Feshbach projection operator formalism. The regime of overlapping resonances is characterized by non-rigid phases of the ΨEc (expressed quantitatively by the phase rigidity ρ). They determine the internal impurity of an open quantum system. Here, level repulsion passes into width bifurcation (resonance trapping): a dynamical phase transition takes place which is caused by the feedback between environment and system. In the third part, the internal impurity of open quantum systems is considered by means of concrete examples. Bound states in the continuum appearing at certain parameter values can be used in order to stabilize open quantum systems. Of special interest are the consequences of the non-rigidity of the phases of λ not only for the problem of dephasing, but also for the dynamical phase transitions and questions related to them such as phase lapses and enhancement of observables.
705 citations
TL;DR: In this paper, the authors introduce the general methods to calculate the entanglement entropy for free fields, within the Euclidean and the real-time formalisms, and describe the particular examples which have been worked out explicitly in two, three and more dimensions.
Abstract: In this paper, we first introduce the general methods to calculate the entanglement entropy for free fields, within the Euclidean and the real-time formalisms. Then, we describe the particular examples which have been worked out explicitly in two, three and more dimensions.
686 citations
TL;DR: In this paper, the properties of reduced density matrices for free fermionic or bosonic many-particle systems in their ground state are reviewed for various one-dimensional situations, including also the evolution after global or local quenches.
Abstract: We review the properties of reduced density matrices for free fermionic or bosonic many-particle systems in their ground state. Their basic feature is that they have a thermal form and thus lead to a quasi-thermodynamic problem with a certain free-particle Hamiltonian. We discuss the derivation of this result, the character of the Hamiltonian and its eigenstates, the single-particle spectra and the full spectra, the resulting entanglement and in particular the entanglement entropy. This is done for various one- and two-dimensional situations, including also the evolution after global or local quenches.
520 citations
TL;DR: In this article, the authors derived the thermodynamic Bethe ansatz equations which should control the spectrum of the planar AdS5/CFT4 correspondence, and the associated set of universal functional relations (Y-system) satisfied by the exponentials of the TBA pseudoenergies.
Abstract: Moving from the mirror theory Bethe?Yang equations proposed by Arutyunov and Frolov, we derive the thermodynamic Bethe ansatz equations which should control the spectrum of the planar AdS5/CFT4 correspondence. The associated set of universal functional relations (Y-system) satisfied by the exponentials of the TBA pseudoenergies is deduced, confirming the structure inferred by Gromov, Kazakov and Vieira.
459 citations
TL;DR: In this article, generalized Camassa-Holm-type equations with infinite hierarchies of higher symmetries are classified as negative flows of integrable quasi-linear scalar evolution equations of orders 2, 3 and 5.
Abstract: We classify generalized Camassa–Holm-type equations which possess infinite hierarchies of higher symmetries. We show that the obtained equations can be treated as negative flows of integrable quasi-linear scalar evolution equations of orders 2, 3 and 5. We present the corresponding Lax representations or linearization transformations for these equations. Some of the obtained equations seem to be new.
454 citations
TL;DR: This work introduces several families of such states in terms of the known renormalization procedures, and highlights some of their properties, and shows how they can be used to describe a variety of systems.
Abstract: We review different descriptions of many-body quantum systems in terms of tensor product states. We introduce several families of such states in terms of the known renormalization procedures, and show that they naturally arise in that context. We concentrate on matrix product states, tree tensor states, multiscale entanglement renormalization ansatz and projected entangled pair states. We highlight some of their properties, and show how they can be used to describe a variety of systems.
403 citations
TL;DR: In this article, the authors review the recent advances towards finding the spectrum of the AdS5? S5 superstring and thoroughly explain the theoretical techniques which should be useful for the ultimate solution of the spectral problem.
Abstract: We review the recent advances towards finding the spectrum of the AdS5 ? S5 superstring. We thoroughly explain the theoretical techniques which should be useful for the ultimate solution of the spectral problem. In certain cases our exposition is original and cannot be found in the existing literature. The present part I deals with foundations of classical string theory in AdS5 ? S5, light-cone perturbative quantization and the derivation of the exact light-cone world-sheet scattering matrix.
TL;DR: In this paper, the dynamics of kinetically constrained models of glass formers were investigated by analyzing the statistics of trajectories of the dynamics, or histories, using large deviation function methods, and it was shown that these models exhibit a first-order dynamical transition between active and inactive dynamical phases.
Abstract: We investigate the dynamics of kinetically constrained models of glass formers by analysing the statistics of trajectories of the dynamics, or histories, using large deviation function methods. We show that, in general, these models exhibit a first-order dynamical transition between active and inactive dynamical phases. We argue that the dynamical heterogeneities displayed by these systems are a manifestation of dynamical first-order phase coexistence. In particular, we calculate dynamical large deviation functions, both analytically and numerically, for the Fredrickson–Andersen model, the East model, and constrained lattice gas models. We also show how large deviation functions can be obtained from a Landau-like theory for dynamical fluctuations. We discuss possibilities for similar dynamical phase-coexistence behaviour in other systems with heterogeneous dynamics.
TL;DR: It is demonstrated that coupling of DNA recognition with conformational transition within the protein‐DNA complex is essential for fast search and a new mechanism for local distance-dependent search that is likely essential in bacteria is proposed.
Abstract: A number of vital biological processes rely on fast and precise recognition of a specific DNA sequence (site) by a protein. How can a protein find its site on a long DNA molecule among 10 6 ‐10 9 decoy sites? Here, we present our recent studies of the protein‐DNA search problem. Seminal biophysical works suggested that the protein‐DNA search is facilitated by 1D diffusion of the protein along DNA (sliding). We present a simple framework to calculate the mean search time and focus on several new aspects of the process such as the roles of DNA sequence and protein conformational flexibility. We demonstrate that coupling of DNA recognition with conformational transition within the protein‐DNA complex is essential for fast search. To approach the complexity of the in vivo environment, we examine how the search can proceed at realistic DNA concentrations and binding constants. We propose a new mechanism for local distance-dependent search that is likely essential in bacteria. Simulations of the search on tightly packed DNA and crowded DNA demonstrate that our theoretical framework can be extended to correctly predicts search time in such complicated environments. We relate our findings to a broad range of experiments and summarize the results of our recent singlemolecule studies of a eukaryotic protein (p53) sliding along DNA.
TL;DR: In this article, the authors derived the hydrodynamic equations governing the density and velocity fields from the microscopic dynamics, in the framework of the associated Boltzmann equation, and showed that the homogeneous flow is found to be stable far from the transition line, but it becomes unstable with respect to finite-wavelength perturbations close to the transition.
Abstract: Considering a gas of self-propelled particles with binary interactions, we derive the hydrodynamic equations governing the density and velocity fields from the microscopic dynamics, in the framework of the associated Boltzmann equation. Explicit expressions for the transport coefficients are given, as a function of the microscopic parameters of the model. We show that the homogeneous state with zero hydrodynamic velocity is unstable above a critical density (which depends on the microscopic parameters), signalling the onset of a collective motion. Comparison with numerical simulations on a standard model of self-propelled particles shows that the phase diagram we obtain is robust, in the sense that it depends only slightly on the precise definition of the model. While the homogeneous flow is found to be stable far from the transition line, it becomes unstable with respect to finite-wavelength perturbations close to the transition, implying a non-trivial spatio-temporal structure for the resulting flow. We find solitary wave solutions of the hydrodynamic equations, quite similar to the stripes reported in direct numerical simulations of self-propelled particles.
TL;DR: An efficient quantum private comparison protocol for comparing information of equality with the help of a third party (TP) is proposed, which can ensure fairness, efficiency and security.
Abstract: Following some ideas of the quantum secret sharing (QSS) protocol (2008, Phys. Lett. A 372, 1957), we propose an efficient quantum private comparison (QPC) protocol for comparing information of equality with the help of a third party (TP). The protocol can ensure fairness, efficiency and security. The protocol is fair, which means that one party knows the sound result of the comparison if and only if the other one knows the result. The protocol is efficient with the help of the TP for calculating. However, the TP cannot learn any information about the players' respective private inputs and even about the comparison result and cannot collude with any player. The protocol is secure for the two players, that is, any information about their respective secret inputs will not leak except the final computation result. A precise proof of security of the protocol is presented. Applications of this protocol may include private bidding and auctions, secret ballot elections, commercial business, identification in a number of scenarios and so on.
TL;DR: In this article, a unified classification of conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime is presented, and a family of infinite-dimensional Lie algebras labeled by a rational "dynamical exponent", z.
Abstract: This paper provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton–Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei structure. They form a family of infinite-dimensional Lie algebras labeled by a rational 'dynamical exponent', z. The Schrodinger–Virasoro algebra of Henkel et al corresponds to z = 2. Viewed as projective Newton–Cartan symmetries, they yield, for timelike geodesics, the usual Schrodinger Lie algebra, for which z = 2. For lightlike geodesics, they yield, in turn, the Conformal Galilean Algebra (CGA) of Lukierski, Stichel and Zakrzewski (alias '' of Henkel), with z = 1. Physical systems realizing these symmetries include, e.g. classical systems of massive and massless non-relativistic particles, and also hydrodynamics, as well as Galilean electromagnetism.
TL;DR: In this article, a review of the recent progress on the study of entropy of entanglement in many-body quantum systems is presented, focusing on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and, more generally, on the concept of area law.
Abstract: We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and, more generally, on the concept of area law. We also briefly describe the relation between entanglement and the presence of impurities, the idea of particle entanglement, the evolution of entanglement along renormalization group trajectories, the dynamical evolution of entanglement and the fate of entanglement along a quantum computation.
TL;DR: In this paper, an infinite family of exactly solvable and integrable potentials on a plane is introduced, and all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular cases of this family.
Abstract: An infinite family of exactly solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular cases of this family. The underlying algebraic structure of the new potentials is revealed as well as its hidden algebra. We conjecture that all members of the family are also superintegrable and demonstrate this for the first few cases. A quasi-exactly-solvable and integrable generalization of the family is found.
TL;DR: In this paper, the authors describe non-Abelian generalizations of the Kuramoto model for any classical compact Lie group and identify their main properties, including the nonlinear evolution equations maintaining the unitarity of all variables which therefore evolve on the compact manifold of U(n).
Abstract: We describe non-Abelian generalizations of the Kuramoto model for any classical compact Lie group and identify their main properties. These models may be defined on any complex network where the variable at each node is an element of the unitary group U(n), or a subgroup of U(n). The nonlinear evolution equations maintain the unitarity of all variables which therefore evolve on the compact manifold of U(n). Synchronization of trajectories with phase locking occurs as for the Kuramoto model, for values of the coupling constant larger than a critical value, and may be measured by various order and disorder parameters. Limit cycles are characterized by a frequency matrix which is independent of the node and is determined by minimizing a function which is quadratic in the variables. We perform numerical computations for n = 2, for which the SU(2) group manifold is S3, for a range of natural frequencies and all-to-all coupling, in order to confirm synchronization properties. We also describe a second generalization of the Kuramoto model which is formulated in terms of real m-vectors confined to the (m − 1)-sphere for any positive integer m, and investigate trajectories numerically for the S2 model. This model displays a variety of synchronization phenomena in which trajectories generally synchronize spatially but are not necessarily phase-locked, even for large values of the coupling constant.
TL;DR: In this article, the authors formulated non-commutative quantum mechanics as a quantum system on the Hilbert space of Hilbert and applied it to the free particle and harmonic oscillator in two dimensions.
Abstract: In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert?Schmidt operators acting on non-commutative configuration space. It is argued that the standard quantum mechanical interpretation based on positive operator valued measures, provides a sufficient framework for the consistent interpretation of this quantum system. The implications of this formalism for rotational and time reversal symmetry are discussed. The formalism is applied to the free particle and harmonic oscillator in two dimensions and the physical signatures of non-commutativity are identified.
TL;DR: In this paper, a small-correlation expansion was proposed to solve the inverse Ising problem and find a set of couplings and fields corresponding to a given set of correlations and magnetizations.
Abstract: We present a systematic small-correlation expansion to solve the inverse Ising problem and find a set of couplings and fields corresponding to a given set of correlations and magnetizations. Couplings are calculated up to the third order in the correlations for generic magnetizations and to the seventh order in the case of zero magnetizations; in addition, we show how to sum some useful classes of diagrams exactly. The resulting expansion outperforms existing algorithms on the Sherrington–Kirkpatrick spin-glass model.
TL;DR: The need to bring together the general encounter problem within foraging theory, as a mean for making progress in the biological understanding of random searching, is stressed.
Abstract: Random walk methods and diffusion theory pervaded ecological sciences as methods to analyze and describe animal movement. Consequently, statistical physics was mostly seen as a toolbox rather than as a conceptual framework that could contribute to theory on evolutionary biology and ecology. However, the existence of mechanistic relationships and feedbacks between behavioral processes and statistical patterns of movement suggests that, beyond movement quantification, statistical physics may prove to be an adequate framework to understand animal behavior across scales from an ecological and evolutionary perspective. Recently developed random search theory has served to critically re-evaluate classic ecological questions on animal foraging. For instance, during the last few years, there has been a growing debate on whether search behavior can include traits that improve success by optimizing random (stochastic) searches. Here, we stress the need to bring together the general encounter problem within foraging theory, as a mean for making progress in the biological understanding of random searching. By sketching the assumptions of optimal foraging theory (OFT) and by summarizing recent results on random search strategies, we pinpoint ways to extend classic OFT, and integrate the study of search strategies and its main results into the more general theory of optimal foraging.
TL;DR: In this paper, the authors review the use of symplectic invariants to solve matrix models' loop equations in the so-called topological expansion, and further extend beyond the context of matrix models.
Abstract: We review the method of symplectic invariants recently introduced to solve matrix models' loop equations in the so-called topological expansion, and further extended beyond the context of matrix models. For any given spectral curve, one defines a sequence of differential forms and a sequence of complex numbers Fg called symplectic invariants. We recall the definition of Fg's and we explain their main properties, in particular symplectic invariance, integrability, modularity, as well as their limits and their deformations. Then, we give several examples of applications, in particular matrix models, enumeration of discrete surfaces (maps), algebraic geometry and topological strings, and non-intersecting Brownian motions.
TL;DR: In this paper, a twisted version of the Yang-Baxter equation, called the Hom-Yang -Baxter Equation (HYBE), is studied, motivated by Hom-Lie algebras.
Abstract: We study a twisted version of the Yang–Baxter equation, called the Hom–Yang–Baxter equation (HYBE), which is motivated by Hom–Lie algebras. Three classes of solutions of the HYBE are constructed, one from Hom–Lie algebras and the others from Drinfeld's (dual) quasi-triangular bialgebras. Each solution of the HYBE can be extended to operators that satisfy the braid relations. Assuming an invertibility condition, these operators give a representation of the braid group.
TL;DR: In this article, the authors review the construction of soliton solutions for the KdV-type lattice equations and use those results to construct N-soliton solutions for all lattice problems in the ABS list except for the elliptic case.
Abstract: In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues of integrable partial differential equations in 1+1 dimensions. In the scalar (i.e. single-field) case, there now exist classification results by Adler, Bobenko and Suris (ABS) leading to some new examples in addition to the lattice equations 'of KdV type' that were known since the late 1970s and early 1980s. In this paper, we review the construction of soliton solutions for the KdV-type lattice equations and use those results to construct N-soliton solutions for all lattice equations in the ABS list except for the elliptic case of Q4, which is left to a separate treatment.
TL;DR: In this article, the expected values of a fermionic basis of quasi-local operators, in the infinite volume limit while keeping the Matsubara (or Trotter) direction finite, were derived.
Abstract: We address the problem of computing temperature correlation functions of the XXZ chain, within the approach developed in our previous works. In this paper we calculate the expected values of a fermionic basis of quasi-local operators, in the infinite volume limit while keeping the Matsubara (or Trotter) direction finite. The result is expressed in terms of two basic quantities: a ratio ρ(ζ) of transfer matrix eigenvalues and a nearest neighbour correlator ω(ζ, ξ). We explain that the latter is interpreted as the canonical second kind differential in the theory of deformed Abelian integrals.
TL;DR: In this paper, a review of the literature on quantum entanglement in (1 + 1)-dimensional systems with a single impurity or a boundary is presented, along with a connection to topological entropy.
Abstract: We review research on a number of situations where a quantum impurity or a physical boundary has an interesting effect on entanglement entropy. Our focus is mainly on impurity entanglement as it occurs in one-dimensional systems with a single impurity or a boundary, in particular quantum spin models, but generalizations to higher dimensions are also reviewed. Recent advances in the understanding of impurity entanglement as it occurs in the spin-boson and Kondo impurity models are discussed along with the influence of boundaries. Particular attention is paid to (1 + 1)-dimensional models where analytical results can be obtained for the case of conformally invariant boundary conditions and a connection to topological entanglement entropy is made. New results for the entanglement in systems with mixed boundary conditions are presented. Analytical results for the entanglement entropy obtained from Fermi liquid theory are also discussed as well as several different recent definitions of the impurity contribution to the entanglement entropy.
TL;DR: In this paper, the traveling wave solutions of nonlinear evolution equations in mathematical physics via the (3+1)-dimensional potential-YTSF equation, the 3+1-dimensional modified KdV-Zakharov-Kuznetsev equation, and the (1+ 1)-dimensional Kadomtsev-Petviashvili equation were constructed by using a generalized -expansion method.
Abstract: In this paper, we construct new traveling wave solutions of some nonlinear evolution equations in mathematical physics via the (3+1)-dimensional potential-YTSF equation, the (3+1)-dimensional modified KdV–Zakharov–Kuznetsev equation, the (3+1)-dimensional Kadomtsev–Petviashvili equation and the (1+1)-dimensional KdV equation by using a generalized -expansion method, where G = G(ξ) satisfies the Jacobi elliptic equation [G'(ξ)]2 = P(G). Here, we assume that P(G) is a polynomial of fourth order. Many new exact solutions in terms of the Jacobi elliptic functions are obtained.
TL;DR: In this article, the thermalization process of the 2D Kitaev model is studied within the Markovian weak coupling approximation, and it is shown that its largest relaxation time is bounded from above by a constant independent of the system size and proportional to exp(2Δ/kT), where Δ is an energy gap over the four-fold degenerate ground state.
Abstract: The thermalization process of the 2D Kitaev model is studied within the Markovian weak coupling approximation. It is shown that its largest relaxation time is bounded from above by a constant independent of the system size and proportional to exp(2Δ/kT), where Δ is an energy gap over the four-fold degenerate ground state. This means that the 2D Kitaev model is not an example of a memory, neither quantum nor classical.