The existence of a phase transition in classical antiferromagnetic models

For a wide class of antiferromagnetic models we prove the existence of a phase transition using an extended Peierls argument, taking into account a result of Dobrushin [R. L. Dobrushin,Funct. Anal. Appl. 2:44 (1968); in English,2:302 (1968)] for an antiferromagnetic Ising model and the results of Malyshev [V. Malyshev,Comm. Math. Phys. 40:75–82 (1975)] for ferromagnetic models (such as the anisotropic rotator). In particular we review a result of Fröhlich, Israel, Lieb, and Simon [J. Fröhlichet al., J. Stat. Phys. 22(3):297–347 (198)] obtained when reflection positivity holds.     

“Solidification” in a soluble model of bosons on a one-dimensional lattice: The “Boson-Hubbard chain”

Lieb and Liniger's soluble model of the 1-D Bose gas is put on a lattice, becoming a “boson-Hubbard model”. It remains soluble by the Bethe ansatz. When the coupling exceeds a critical value ($\text{U}\text{2πT}\text{)>}\text{2√3}\text{π}$, a gap is present when the density n bosons per site is 1.     

Pinning Model in Random Correlated Environment: Appearance of an Infinite Disorder Regime

We study the influence of a correlated disorder on the localization phase transition in the pinning model (Random polymer models, 2007). When correlations are strong enough, an infinite disorder regime arises: large and frequent attractive regions appear in the environment. We present here a pinning model in random binary ( $\{-1,1\}$ -valued) environment. Defining infinite disorder via the requirement that the probability of the occurrence of a large attractive region is sub-exponential in its size, we prove that it coincides with the fact that the critical point is equal to its minimal possible value, namely $h_c(\beta )=-\beta $ . We also stress that in the infinite disorder regime, the phase transition is smoother than in the homogeneous case, whatever the critical exponent of the homogeneous model is: disorder is therefore always relevant. We illustrate these results with the example of an environment based on the sign of a Gaussian correlated sequence, in which we show that the phase transition is of infinite order in presence of infinite disorder. Our results contrast with results known in the literature, in particular in the case of an IID disorder, where the question of the influence of disorder on the critical properties is answered via the so-called Harris criterion, and where a conventional relevance/irrelevance picture holds.     

Electronic state on the surface in the strongly correlated electron systems

In order to clarify the tunneling spectroscopy in high-T_c cuprates, we study electronic state of the surface in the strongly correlated electron systems. First, we obtain Green's function of strongly correlated normal bulk system using the fluctuation exchange (FLEX) approximation. Next, we insert infinite potential into the bulk system and obtain Green's function of surface. We find that the density of states (DOS) in strongly correlated bulk systems are different from that on the surface, and the difference decreases as the magnitude of Coulomb interaction (U) increases.     

Statefinder Diagnostic for Modified Chaplygin Gas with the Sign-Changeable Interaction

Statefinder diagnostic is a useful method which can distinguish one dark energy model from the others. In this paper, we apply this method to the modified Chaplygin gas (MCG) model with the sign-changeable interaction in which the interaction term Q can change its sign from Q<0 to Q>0 as the universe expands. We plot the evolutionary trajectories of this model in the statefinder parameter-planes, and it is found that the coupling constant β plays a significant role from the statefinder viewpoint. Furthermore, we can conclude that the statefinder diagnostic can not only discriminate the model with different coupling constant but also distinguish the model from other dark energy models.     

Local probes strongly favor ΛCDM against power-law and R_h=ct universe

We constrain three cosmological models – the concordance cold dark matter plus cosmological constant(ΛCDM) model, the power-law(PL) model, and the Rh =ct model – using the available local probes, which include the JLA compilation of type-Ia supernovae(SNe Ia), the direct measurement of the Hubble constant(H_(z)), and the baryon acoustic oscillations(BAO). For the ΛCDM model, we consider two different cases, i.e. zero and non-zero spatial curvature. We find that by using the JLA alone, the ΛCDM and PL models are indistinguishable, but the Rh =ct model is strongly disfavored. If we combine JLA+H_(z), the ΛCDM model is strongly favored over the other two models. The combination of all three datasets supports ΛCDM as the best model. We also use the low-redshift(z 0.2) data to constrain the deceleration parameter using the cosmography method, and find that only the ΛCDM model is consistent with cosmography. However, there is no strong evidence to distinguish between flat and non-flatΛCDM models by using the local data alone.     

Quasiparticles in a strongly correlated liquid with the fermion condensate: applications to high-temperature superconductors

A model of a strongly correlated electron liquid based on fermion condensation (FC) is extended to high-temperature superconductors. Within our model, the appearance of FC presents a boundary separating the region of a strongly interacting electron liquid from the region of a strongly correlated electron liquid. We study the superconductivity of a strongly correlated liquid and show that, under certain conditions, the superconductivity vanishes at temperatures T > T _c ≈ T _node, with the superconducting gap being smoothly transformed into a pseudogap. As a result, the pseudogap occupies only a part of the Fermi surface. The gapped area shrinks with increasing the temperature and vanishes at T = _T*. The single-particle excitation width is also studied. The quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by the effective masses and, intersecting near the binding energy that is on the order of the superconducting gap. It is argued that this strong change of the quasiparticle dispersion upon binding can be enhanced in underdoped samples because of strengthening the FC influence. The FC phase transition in the presence of the superconductivity is examined, and it is shown that this phase transition can be considered as driven by the kinetic energy.     

Data processing for the sandwiched Rényi divergence: a condition for equality

The \(\alpha \)-sandwiched Rényi divergence satisfies the data processing inequality, i.e. monotonicity under quantum operations, for \(\alpha \ge 1/2\). In this article, we derive a necessary and sufficient algebraic condition for equality in the data processing inequality for the \(\alpha \)-sandwiched Rényi divergence for all \(\alpha \ge 1/2\). For the range \(\alpha \in [1/2,1)\), our result provides the only condition for equality obtained thus far. To prove our result, we first consider the special case of partial trace and derive a condition for equality based on the original proof of the data processing inequality by Frank and Lieb (J Math Phys 54(12):122201, 2013) using a strict convexity/concavity argument. We then generalize to arbitrary quantum operations via the Stinespring Representation Theorem. As applications of our condition for equality in the data processing inequality, we deduce conditions for equality in various entropic inequalities. We formulate a Rényi version of the Araki–Lieb inequality and analyze the case of equality, generalizing a result by Carlen and Lieb (Lett Math Phys 101(1):1–11, 2012) about equality in the original Araki–Lieb inequality. Furthermore, we prove a general lower bound on a Rényi version of the entanglement of formation and observe that it is attained by states saturating the Rényi version of the Araki–Lieb inequality. Finally, we prove that the known upper bound on the entanglement fidelity in terms of the usual fidelity is saturated only by pure states.     

Phase behaviors of strongly correlated Fermi gases in one-dimensional confinements

We report on the ground state of models for strongly correlated one-dimensional Fermi systems by means of theoretical studies of two-component atomic Fermi gases in highly anisotropic harmonic traps. In this context, we consider (i) the Gaudin-Yang model for a Luttinger liquid with repulsive interactions, including an analysis of the emergence of Wigner molecules in the 2k _F → 4k _F crossover, and (ii) the lattice Hubbard model yielding Luttinger liquid and Mott insulator or band-insulator phases for repulsive interactions and the Luther-Emery phase for attractive interactions, including in the former case an analysis of the role of disorder. Our calculations use novel versions of density and spin-density functional theory and a density-matrix renormalization-group technique. We also discuss preliminary results and future perspectives in the study of nonsymmetric two-component Fermi gases.     

Correlation functions for a strongly correlated boson system

The correlation functions for a strongly correlated exactly solvable one-dimensional boson system on a finite chain as well as in the thermodynamic limit are calculated explicitly. This system, which we call the phase model, is the strong coupling limit of the integrable q-boson hopping model. The results are presented as determinants.     

Bounds on the hadronic matrix element in theK^0 - \bar K^0 transition amplitude

The hadronic matrix element in the \(K^0 - \bar K^0 \) transition amplitude has been calculated in a variety of models and doubt has arisen as to its size and sign. In this paper the present experimental constraints on the Kobayashi-Maskawa matrix elements are used to establish the positive sign of the hadronic matrix element in the six quark model and to place bounds on its magnitude. The bounds are 0.04<B<1.2 whereB=+1 gives the vacuum saturation estimate of the hadronic matrix element. The experimental information also restricts the number of possible solutions to theK _s -K _l mass difference and the CP parameter in the Kobayashi-Maskawa model.     

Strongly coupled massive QCD3 and frustrated Heisenberg antiferromagnets: fractional statistics and chiral-spin order

Strongly coupled massive SU(N_C) and U(N_C) QCD₃ on a lattice is studied using the 1/N_C expansion. The quark mass terms have a definite sign in the present model, and therefore the system explicitly breaks the parity symmetry. The continuum counterpart generates the Maxwell + Chern-Simons theory by integrating out the quark field. In the present paper, we shall integrate out the gauge fields using the strong-coupling expansion and obtain a frustrated quantum Heisenberg model as an effective model. The ground state of the above effective quantum spin model is studied using the large-N_C approximation. There are two phases; one is a Neel-ordered state and the other is a state with a chiral-spin order. It is explicitly shown that the chiral-spin ordered state corresponds to a state with spontaneous generation of color magnetic flux in the original theory and fractional statistics appears in that phase. This result strongly suggests that there are (at least) two phases in the massive QCD₃ and Maxwell-CS theory. One is the confinement phase and the other is the perturbative deconfinement phase with fractional-statistics excitations.     

Formation of exotic states in the <Emphasis Type="Italic">s–d</Emphasis> exchange and <Emphasis Type="Italic">t–J</Emphasis> models

Different scenarios of the implementation of the two-band model in systems of strongly correlated electrons, including frustrated magnetic systems, high-temperature superconductors, and Kondo lattices, are considered. The interaction of current carriers with magnetic moments in the representations of pseudofermions or Schwinger bosons describing the spinon excitations is studied on the basis of the derived Hamiltonians of the s–d exchange and t–J models within the formalism of many-electron Hubbard X operators.     

Fractal diffusion in smooth dynamical systems with virtual invariant curves

Preliminary results of extensive numerical experiments with a family of simple models specified by the smooth canonical strongly chaotic 2D map with global virtual invariant curves are presented. We focus on the statistics of the diffusion rate D of individual trajectories for various fixed values of the model perturbation parameters K and d. Our previous conjecture on the fractal statistics determined by the critical structure of both the phase space and the motion is confirmed and studied in some detail. In particular, we find additional characteristics of what we earlier termed the virtual invariant curve diffusion suppression, which is related to a new very specific type of critical structure. A surprising example of ergodic motion with a “hidden” critical structure strongly affecting the diffusion rate was also encountered. At a weak perturbation (K ? 1), we discovered a very peculiar diffusion regime with the diffusion rate D=K ²/3 as in the opposite limit of a strong (K ? 1) uncorrelated perturbation, but in contrast to the latter, the new regime involves strong correlations and exists for a very short time only. We have no definite explanation of such a controversial behavior.     

Effective action for strongly correlated electron systems

The su(2|1) coherent-state path-integral representation of the partition function of the t-J model of strongly correlated electrons is derived at finite doping. The emergent effective action is compared to the one proposed earlier on phenomenological grounds by Shankar to describe holes in an antiferromagnet [R. Shankar, Nucl. Phys. B 330 (1990) 433]. The t-J model effective action is found to have an important “extra” factor with no analogue in Shankar?s action. It represents the local constraint of no double electron occupancy and reflects the rearrangement of the underlying phase-space manifold due to the presence of strong electron correlation. This important ingredient is shown to be essential to describe the physics of strongly correlated electron systems.     

Two-particle azimuthal and rapidity correlations in intervals of transverse momentum in π+ p-interactions at 250 GeV/c

A multi-dimensional analysis of two-particle correlations in π⁺ p-interactions at 250 GeV/c shows interesting structure. Particularly strong positive shortrange rapidity and azimuthal correlations are observed for low-p _T like sign pairs. This observation is not reproduced by models used for comparison (FRITIOF, DPM, quark gluon (multi)string model). A possible explanation is Bose-Einstein interference not included in these models.     

Spin-polarized zero-energy states in BN/C core–shell quantum dots

Boron-nitride (BN) domains in graphene or graphene domains in BN monolayer offer additional freedoms for tuning the electronic properties of these BN/C nanostructures, which is quite crucial for the applications in nanoscale devices. Based on first-principles calculations combined with a simple Hubbard model, we show that the electron zero-energy states (ZESs) of BN/graphene core–shell quantum dots (QDs) in triangular shapes can be well tuned by varying the size and topology of each domain. The net spin of the systems is dominated by the graphene segment which can be described by a Lieb?s theorem. We also demonstrated that a π-electron Hubbard model within a mean-field approximation is implementable in dealing with the electron spin-polarization of BN/C hetero-structured graphene-like materials. This provides an efficient theoretical approach for the BN/C systems where electron spin-polarization is involved.     

Remarks on the relation between quantum and classical entropy as proposed by A. Wehrl

Using an inequality of Lieb one can compute a probability distribution which is less mixed than any (z|ωz)dz, where z labels the points of phase space, w is a density matrix, and (z| the appropriate coherent state.     

Statistical mechanics of hydrogen bond networks

The static and dynamic properties of several hydrogen bond network models, based on thesquare ice model of Lieb [Phys. Rev.162, 162 (1967)] are studied. The two dimensionalsquare water (SW) model and the three-dimensioaalbrick water (BW) model were analyzed by means of Monte Carlo simulations. A simplified vesion of SW (simplified square water, SSW) can be solved exactly. All models yield similar thermodynamic results which can be derived-alternatively-from an independent bond approach due to Angell [J. Chem. Phys.75, 3698 (1971)]. We suggest the existence of a universality class of hydrogen bond networks that can be described by this theory, and which may include the liquid state of water. The mean lifetime of a hydrogen bond exhibits an Arrhenius temperature dependence. Comparison with experimental data on water provides an absolute time scale for the Monte Carlo simulations. The possible use of these models in simulations of protein-solvent systems is discussed.