The State(s) of Replica Symmetry Breaking: Mean Field Theories vs. Short-Ranged Spin Glasses

We prove the impossibility of recent attempts to decouple the Replica Symmetry Breaking (RSB) picture for finite-dimensional spin glasses from the existence of many thermodynamic (i.e., infinite-volume) pure states while preserving another signature RSB feature—space filling relative domain walls between different finite-volume states. Thus revisions of the notion of pure states cannot shield the RSB picture from the internal contradictions that rule out its physical correctness in finite dimensions at low temperature in large finite volume.     

A review of the dynamical susceptibility in different complex systems

The dynamical susceptibility has been introduced to characterize the dynamical heterogeneities in glass forming liquids. We have used it as a tool to investigate the slow dynamics of other disordered systems such as gels, granular media and spin glasses. We review here the results obtained via numerical simulations of different model systems. The comparative study of the behaviour of the dynamical susceptibility sheds some light on the significant differences in the complex slow dynamics of glasses, spin glasses, granular media, irreversible gels, and colloidal gels.     

The Response of Glassy Systems to Random Perturbations: A Bridge Between Equilibrium and Off-Equilibrium

We discuss the response of aging systems with short-range interactions to a class of random perturbations. Although these systems are out of equilibrium, the limit value of the free energy at long times is equal to the equilibrium free energy. By exploiting this fact, we define a new order parameter function, and we relate it to the ratio between response and fluctuation, which is in principle measurable in an aging experiment. For a class of systems possessing stochastic stability, we show that this new order parameter function is intimately related to the static order parameter function, describing the distribution of overlaps between clustering states. The same method is applied to investigate the geometrical organization of pure states. We show that the ultrametric organization in the dynamics implies static ultrametricity, and we relate these properties to static separability, i.e., the property that the measure of the overlap between pure states is essentially unique. Our results, especially relevant for spin glasses, pave the way to an experimental determination of the order parameter function.     

Spin glass models with ferromagnetically biased couplings on the Bethe lattice: analytic solutions and numerical simulations

We derive the zero-temperature phase diagram of spin glass models with a generic fraction of ferromagnetic interactions on the Bethe lattice. We use the cavity method at the level of one-step replica symmetry breaking (1RSB) and we find three phases: a replica-symmetric (RS) ferromagnetic one, a magnetized spin glass one (the so-called mixed phase), and an unmagnetized spin glass one. We are able to give analytic expressions for the critical point where the RS phase becomes unstable with respect to 1RSB solutions: we also clarify the mechanism inducing such a phase transition. Finally we compare our analytical results with the outcomes of a numerical algorithm especially designed for finding ground states in an efficient way, stressing weak points in the use of such numerical tools for discovering RSB effects. Some of the analytical results are given for generic connectivity.     

Exotic and excited-state meson spectroscopy and radiative transitions from lattice QCD

We discuss recent progress in extracting the excited meson spectrum and radiative transition form factors from lattice QCD.We mention results in the charmonium sector,including the first lattice QCD calculation of radiative transition rates involving excited charmonium states,highlighting results for high spin and exotic states.We present recent results on a highly excited isovector meson spectrum from dynamical anisotropic lattices.Using carefully constructed operators we show how the continuum spin of extracted states can be reliably identified and confidently extract excited states,states with exotic quantum numbers and states of high spin.This spectrum includes the first spin-four state extracted from lattice QCD.We conclude with some comments on future prospects.     

Free-Energy Bounds for Hierarchical Spin Models

In this paper we study two non-mean-field (NMF) spin models built on a hierarchical lattice: the hierarchical Edward–Anderson model (HEA) of a spin glass, and Dyson’s hierarchical model (DHM) of a ferromagnet. For the HEA, we prove the existence of the thermodynamic limit of the free energy and the replica-symmetry-breaking (RSB) free-energy bounds previously derived for the Sherrington–Kirkpatrick model of a spin glass. These RSB mean-field bounds are exact only if the order-parameter fluctuations (OPF) vanish: given that such fluctuations are not negligible in NMF models, we develop a novel strategy to tackle part of OPF in hierarchical models. The method is based on absorbing part of OPF of a block of spins into an effective Hamiltonian of the underlying spin blocks. We illustrate this method for DHM and show that, compared to the mean-field bound for the free energy, it provides a tighter NMF bound, with a critical temperature closer to the exact one. To extend this method to the HEA model, a suitable generalization of Griffith’s correlation inequalities for Ising ferromagnets is needed: since correlation inequalities for spin glasses are still an open topic, we leave the extension of this method to hierarchical spin glasses as a future perspective.     

On the branching structure of the tree of states in spin glasses

We review some known results on the nature of the tree of states in spin glasses and we present new results on its topology. We pay particular attention to the so-called continuum limit in which the levels are labeled by a continuous variablex. We also study the dependence on the levelx of the type of branching (bifurcation, trifurcation,...). We show that the statistics of the tree is universal in the continuum limit, i.e., it does not depend on the details of the algorithm used to generate the tree.     

Aging, rejuvenation and memory phenomena in spin glasses

In this paper, we review several important features of the out-of-equilibrium dynamics of spin glasses. Starting with the simplest experiments, we discuss the scaling laws used to describe the isothermal aging observed in spin glasses after a quench down to the low-temperature phase. We report in particular new results on the sub-aging behaviour of spin glasses. We then discuss the rejuvenation and memory effects observed when a spin glass is submitted to temperature variations during aging, from the point of view of both energy landscape pictures and real-space pictures. We highlight the fact that both approaches point out the necessity of hierarchical processes involved in aging. Finally, we report an investigation of the effect of small temperature variations on aging in spin glass samples with various anisotropies which indicates that this hierarchy depends on the spin anisotropy.     

Measuring overlaps in mesoscopic spin glasses via conductance fluctuations

We consider the electronic transport in a mesoscopic metallic spin glass. We show that the distribution of overlaps between spin configurations can be inferred from the reduction of the conductance fluctuations by the magnetic impurities. Using this property, we propose new experimental protocols to probe spin glasses directly through their overlaps.     

Mott transition in kagomé lattice Hubbard model

We investigate the Mott transition in the kagomé lattice Hubbard model using a cluster extension of dynamical mean field theory. The calculation of the double occupancy, the density of states, and the static and dynamical spin correlation functions demonstrates that the system undergoes the first-order Mott transition at the Hubbard interaction U/W approximately 1.4 (W:bandwidth). In the metallic phase close to the Mott transition, we find the strong renormalization of three distinct bands, giving rise to the formation of heavy quasiparticles with strong frustrated interactions. It is elucidated that the quasiparticle states exhibit anomalous behavior in the temperature-dependent spin correlation functions.     

Exact results for spin dynamics and fractionalization in the Kitaev Model

We present certain exact analytical results for dynamical spin correlation functions in the Kitaev Model. It is the first result of its kind in nontrivial quantum spin models. The result is also novel: in spite of the presence of gapless propagating Majorana fermion excitations, dynamical two spin correlation functions are identically zero beyond nearest neighbor separation. This shows existence of a gapless but short range spin liquid. An unusual, all energy scale fractionalization of a spin-flip quanta, into two infinitely massive pi fluxes and a dynamical Majorana fermion, is shown to occur. As the Kitaev Model exemplifies topological quantum computation, our result presents new insights into qubit dynamics and generation of topological excitations.     

一维量子子自自旋链中拓扑有序态的物理描述

一维量子多体系统是凝聚态物理学中的重要研究方向之一,其中的新奇量子物态则是重要的研究课题。本文我们首先简要回顾一维量子整数自旋链体系的相关研究背景,然后提出一类SO(n)对称的严格可解量子自旋链模型及其矩阵乘积基态。当奇数n≥3时,体系的基态为Haldane相。利用这类态中隐藏的稀薄反铁磁序,我们找到了刻画这类态的非局域弦序参量,并在隐藏拓扑对称性的统一框架下解释了稀薄反铁磁序以及边缘态等奇特现象的起源。当偶数n≥4时,体系的基态为二聚化态。这些态属于破缺平移对称性的非Haldane相,但同样具有隐藏的反铁磁序。通过这些严格解的研究,我们还得到了一维SO(n)对称的双线性–双二次模型的基态相图,并发现在n≥5时,一维SO(n)对称的反铁磁海森堡模型的基态处于二聚化相中。基于以上这些结果,我们推广构造了一维平移不变且包含李群G对称性的Valence BondState(VBS)态,并利用其矩阵乘积表示讨论了对应哈密顿量的构造方法。对于自旋为S的量子整数自旋链,我们研究了两类具有不同拓扑属性的VBS类,前一类VBS态的边缘态处于SU(2)自旋J的不可约表示,后一类VBS态的边缘态为SO(2S+1)旋量。在前一类态中,我们以自旋为1的费米型VBS态为例构造了对应的哈密顿量。对后一类态,我们证明了它们等价于SO(2S+1)矩阵乘积态,从而揭示了呈展对称性的起源和边缘态的性质。我们还推广了SO(5)对称的玻色型和费米型VBS态,并探讨了它们的拓扑刻画方式。     

Low temperature correlation functions in integrable models: Derivation of the large distance and time asymptotics from the form factor expansion

We propose an approach to the problem of low but finite temperature dynamical correlation functions in integrable one-dimensional models with a spectral gap. The approach is based on the analysis of the leading singularities of the operator matrix elements and is not model specific. We discuss only models with well-defined asymptotic states. For such models the long time, large distance asymptotics of the correlation functions fall into two universality classes. These classes differ primarily by whether the behavior of the two-particle S-matrix at low momenta is diagonal or corresponds to pure reflection. We discuss similarities and differences between our results and results obtained by the semi-classical method suggested by Sachdev and Young [S. Sachdev, A.P. Young, Phys. Rev. Lett. 78 (1997) 2220].     

Spin dynamics for 2d Heisenberg antiferromagnets with combined easy-plane and Dzyaloshinsky interactions

We investigate the spin dynamics of the classical two-dimensional easy-plane Heisenberg antiferromagnet with an additional Dzyaloshinsky interaction, which serves as a simple model for Langmuir-Blodgett films of Mn (C₁₈H₃₅O₂)₂. By mapping the system onto a pure easy-plane model we discuss the corresponding spin wave and vortex dynamics. The additional Dzyaloshinsky interaction forces all spins to cant in a certain direction, which is the same for neighboring spins on different sublattices. This canting causes the presence of a second spin wave peak in the dynamical in-plane correlation function below the Kosterlitz-Thouless transition temperature T_KT and a second vortex central peak above T_KT. Using a vortex gas approach we explicitly calculate the contribution of the free vortices to several dynamical correlation functions. These results are compared to a combined Monte Carlo-Molecular Dynamics simulation on square lattices with different sizes. We also discuss the relevance of this simple model for describing the spin dynamics of Mn (C₁₈H₃₅O₂)₂.     

Anderson impurity in a correlated conduction band

We investigate the physics of a magnetic impurity with spin 1/2 in a correlated metallic host. Describing the band by a Hubbard Hamiltonian, the problem is analyzed using dynamical mean-field theory in combination with Wilson's nonperturbative numerical renormalization group. We present results for the single-particle density of states and the dynamical spin susceptibility at zero temperature. New spectral features (side peaks) are found which should be observable experimentally. In addition, we find a general enhancement of the Kondo scale due to correlations. Nevertheless, in the metallic phase, the Kondo scale always vanishes exponentially in the limit of small hybridization.     

The Dynamical Evolution of Quantum Correlations in the Two Isolate Spin Particles Coupled to a Common Bath

We study the dynamical evolution of quantum correlations between two central spins independently coupled to a common bath, which are represented by quantum entanglement and quantum discord. According to the results of the exact solution, we show that quantum discord is more robust and includes richer correlation than quantum entanglement due to the nonvanishing quantum correlation in the region of entanglement death, i.e., the separable states maybe contain nonclassical correlations. We discuss the effects of the intrinsic properties of the bath on quantum correlation between the two central spins in the XY and XXZ model baths. At the low temperature, the central system can keep the good quantum correlation. With the more spin number in the bath, the dynamical evolution of quantum correlation can be bounded with the small oscillation and finally approaches a stable value. In addition, we find that the interaction between the central spins and the bath in the z direction has the significant effects on quantum correlation of the central spin system.     

Nonnegative Discrete Symbols and Their Probabilistic Interpretation

We review the quantizer–dequantizer formalism of constructing symbols of the density operators and quantum observables, such as Wigner functions and tomographic-probability distributions. We present a tutorial consideration of the technique of obtaining minimal sets of dequantizers (quorum) related to the observable eigenvalues for one-qubit states. We discuss a generalization of the quantizer–dequantizer scheme on the example of spin-1/2 states. We consider the possibilities of extending the results to two-qubit systems using spin tomograms of the state density matrix.     

Remove Degeneracy in Relativistic Symmetries for Manning-Rosen Plus Quasi-Hellman Potentials by Tensor Interaction

The relativistic Dirac equation under spin and pseudo-spin symmetries is investigated for Manning-Rosen plus quasi-Hellman potentials with tensor interaction. For the first time we consider the Hulthen plus Yukawa for tensor interaction. The Formula method is used to obtain the energy eigen-values and wave functions. We also discuss about the energy eigen-values and the Dirac spinors for the Manning-Rosen plus quasi-Hellman potentials for the spin and pseudo-spin symmetry with Formula method. To show the accuracy of the present model, some numerical results are shown in both pseudo-spin and spin symmetry limits.     

Quantum Correlations in Systems of Indistinguishable Particles

We discuss quantum correlations in systems of indistinguishable particles in relation to entanglement in composite quantum systems consisting of well separated subsystems. Our studies are motivated by recent experiments and theoretical investigations on quantum dots and neutral atoms in microtraps as tools for quantum information processing. We present analogies between distinguishable particles, bosons, and fermions in low-dimensional Hilbert spaces. We introduce the notion of Slater rank for pure states of pairs of fermions and bosons in analogy to the Schmidt rank for pairs of distinguishable particles. This concept is generalized to mixed states and provides a correlation measure for indistinguishable particles. Then we generalize these notions to pure fermionic and bosonic states in higher-dimensional Hilbert spaces and also to the multi-particle case. We review the results on quantum correlations in mixed fermionic states and discuss the concept of fermionic Slater witnesses. Then the theory of quantum correlations in mixed bosonic states and of bosonic Slater witnesses is formulated. In both cases we provide methods of constructing optimal Slater witnesses that detect the degree of quantum correlations in mixed fermionic and bosonic states.     

Controllable coupling and quantum correlation dynamics of two double quantum dots coupled via a transmission line resonator

We propose a theoretical scheme to generate a controllable and switchable coupling between two double-quantum-dot (DQD) spin qubits by using a transmission line resonator (TLR) as a bus system. We study dynamical behaviors of quantum correlations described by entanglement correlation (EC) and discord correlation (DC) between two DQD spin qubits when the two spin qubits and the TLR are initially prepared in X-type quantum states and a coherent state, respectively. We demonstrate that in the EC death regions there exist DC stationary states in which the stable DC amplification or degradation can be generated during the dynamical evolution. It is shown that these DC stationary states can be controlled by initial-state parameters, the coupling, and detuning between qubits and the TLR. We reveal the full synchronization and anti-synchronization phenomena in the EC and DC time evolution, and show that the EC and DC synchronization and anti-synchronization depends on the initial-state parameters of the two DQD spin qubits. It is shown that the initial quantum correlation may be suppressed completely when the evolution time approaches to the infinity in the presence of dissipation. These results shed new light on dynamics of quantum correlations.