Results of an exact 2 scale transformation for two-dimensional lattice systems with O(2) and O(3) symmetry

The diagonal-to-diagonal transfer operator is considered on two-dimensional square lattices. A variational solution treating every second spin in an exact way is shown to yield very encouraging correlation length estimates for T>T_c in the cases of the XY and Heisenberg spin models.     

Superconducting plate in a transverse magnetic field: New state

A model is proposed for describing Cooper pairs near the transition (in temperature and magnetic field) point when their spacing is larger than their size. The essence of the model is as follows: the Ginzburg-Landau functional is written in operator form in terms of field operators of the Bose type so that the average value of the density operator gives the concentration of Cooper pairs, and the same Ginzburg-Landau expression is obtained for the Bose condensate. The model is applied to a superconducting plate with a thickness smaller than the size of a pair in a transverse magnetic field near its upper critical value H _c2. A new state is discovered that is energetically more advantageous in a certain interval in the vicinity of the transition point as compared to the Abrikosov vortex state. The wavefunction of the system in this state is of the type of the Laughlin function used in the fractional quantum Hall effect (naturally, as applied to Cooper pairs as Bose particles in our case) and corresponds to a homogeneous incompressible fluid. The energy of this state is proportional to the first power of quantity (1 ? H/H _c2) in contrast to the energy of the vortex state containing the square of this quantity. The interval of the existence of the new state is the larger, the dirtier the sample.     

Schwinger Bose实现下自旋相干态Wigner函数的特性分析

在Schwinger Bose实现下,引入纠缠态表象及Wigner算符在该表象下的表示,得到自旋相干态的Wigner函数,数值计算画出相空间中Wigner函数的分布图,并加以分析,发现在SchwingerBose实现下自旋相干态确实体现出纠缠特性。     

An effect of the uniaxial strain on the temperature of Bose–Einstein condensation of the intersite bipolarons

We have studied an effect of uniaxial strain to the temperature of Bose–Einstein condensation of intersite bipolarons within the framework of extended Holstein–Hubbard model. Uniaxial lattice strains are taken into an account by introducing a generalized density–displacement type force for electron–lattice interaction. Associating the superconducting critical temperature T_c with the temperature of Bose–Einstein condensation T_BEC of intersite bipolarons we have calculated strain derivatives of T_BEC and satisfactorily explained the results of the experiments on La-based high-T_c films.     

Structural Aspects of the Fermion-Boson Mapping in Two-Dimensional Gauge and Anomalous Gauge Theories with Massive Fermions

Using a synthesis of the functional integral and operator approaches we discuss the fermion-boson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED₂ with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED₂ with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Θ-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content.     

Quantum limit for the atom-light interferometer

The standard quantum limit is calculated for the atom-light interferometer. It is shown that the smallest detectable phase is $$\delta \phi _{\min } = \frac{1}{2}[N_{atoms} + 4N_{photons} )/N_{atoms} N_{photons} ]^{1/2} .$$ Therefore, in practical experiments, the accuracy is limited by the square root of the number of atoms. We propose a novel correlated atom-photon state interferometer which makes a transition to the Heisenberg limit, δφ_min ∝ 1/N _atoms, as the atoms approach a Bose condensate. Such an interferometer may serve as a sensitive probe of the onset of Bose condensation. Finally, we point out that the correlated atom-photon state preparation scheme we propose may be used in a different way to approach the Heisenberg limit for non-Bose-condensed atoms.     

A relation between gauge-invariant formulation of QCD and string theory in two dimensions

We have studied the explicit relation between the gauge-invariant path-ordered operator (POO) and a string field in two dimensions. For this purpose, we use the hamiltonian of two-dimensional quantum chromodynamics reformulated in terms of POO. POO is expanded in a power series of a non-local bosonic operator. We show that such a bosonic operator describes Bars and Hanson's free string field in the second quantization. Interactions among bosonic operators are treated in perturbation theory. The coupling constant is proportional to 1/√N_c.     

On the limits of consistency of Eliashberg theory and the density of states of high-T c superconductors

We make a detailed study of the Eliashberg theory in the coupling region where some fundamental qualitative deviations from the conventional BCS-like behavior begin to appear. These deviations are identified as the onset of a cross-over from BCS superconductivity to Bose condensation. We point out that the beginning of this cross-over occurs when the gap δ _g becomes comparable to the boson energies Ω_ph. This condition traduces the physical constraint that the distance the paired electron covers during the absorption of the virtual boson, cannot be larger than the coherence length. The frontier region of couplings is of the order of λ ≈ 3, and high-T _c, materials are concerned. A clear qualitative indication of the occurrence of a crossover regime should be a dip structure above the gap in the density of states of excitations, and this is one of the most robust characteristics of the high-T _c, superconducting state. Comparing our results with tunneling and photoemission experiments we conclude that high-T _c materials (cuprates and fullerides) are indeed at the beginning of a cross-over from BCS superconductivity to Bose condensation, even though the fermionic nature still prevails. If the Uemura plot is relevant, then the dip should also be present in the other materials that are close to the cross-over regime like heavy Fermion and organic superconductors. In all these materials Ginzburg Landau equations are irrelevant.     

Quantum phase transition in the anisotropic one-dimensional XY model with long-range interactions

In this paper we study the one-dimensional XY model with single ion anisotropy and long-range interaction that decay as a power law. The model has a quantum phase transition, at zero temperature, at a critical value D_c of the anisotropy parameter D. For values of D below D_c we use a self-consistent harmonic approximation. We have found that the critical temperature increases with D for small values of this parameter. For values of D above D_c we use the bond operator technique and calculate the gap as a function of D, at zero temperature.     

Effects of ion doping on magnetism of antiferromagnetic nanoparticles

Based on the Heisenberg model including single-ion anisotropy and using a Green's function technique we have studied the influence of doping effects on magnetization M, Neel temperature T_N and coercive field H_c of antiferromagnetic nanoparticles. We have shown that the experimentally obtained room temperature magnetization M is due to surface or/and doping effects in antiferromagnetic nanoparticles.     

Field induced order in magnetic systems: Marginal case

The bond operator representation and the one-loop renormalization group treatment are used to study the spin-1 Heisenberg antiferromagnetic with single-ion anisotropy and transversal magnetic fields in three-dimensional cubic lattices. We start from a disordered spin-liquid phase to an ordered phase, at a critical field H_c1 above which the system enters an XY-antiferromagnetic phase. This transition is interpreted as belonging to a universality class with a dynamical critical exponent z=1. In this marginal case logarithmic corrections are found to the physical quantities. These theoretical predictions are compared with the scaling of the magnetization as a function of field and temperature for the organic compound NiCl₂-4SC(NH₂)₂.     

On the finiteness of scaling sum rules

The convergence of sum rules relating the matrix elements of local operators to integrals over deep-inelastic structure functions is studied critically. It is found that the matrix elements may always be written as the q² → ? ∞ limit of finite expressions, regardless of the (Regge) asymptotic behavior of the structure functions or the possible occurrence of J = 0 fixed singularities. The correct form of the sum rule for the operator Schwinger term is taken as a paradigm case. It is derived from the Bjorken-Johnson-Low theorem and agrees with the results of parton model and light-cone analyses. It readily encompases the results of second order φ³ theory (where the Schwinger term diverges logarithmically) and second order vector gluon theory (where it vanishes). Sufficient conditions for the finiteness of the operator Schwinger term are the scaling of the longitudinal structure function and the absence of J = 0 fixed singularities with nonpolynomial residues. The treatment is readily applicable to other scaling and fixed q² sum rules needing regulation. A compendium of these is given.     

Remark on the application of the effective hamiltonian method for random systems

We compare two versions of the effective Hamiltonian method applied to random bond systems. In one randomness is treated in a kind of the mean field approximation, whereas in the other the relevant arrangements of bonds are explicitly accounted for. Calculations for three dimensional systems of mixed ferromagnetic Heisenberg and Ising bonds show that although the T_c vs p (concentration of Heisenberg-loke interactions) curve in the second approach lies closer to the results of high temperature series general features in both approxsimations are quite similar.     

On the critical temperature in a Boson-Fermion mixture with attraction between the components

The dependence of the critical temperature shift in the Bose component of a degenerate Bose-Fermi gas mixture in a harmonic trap on the number of bosons and fermions has been obtained on the basis of the effective Hamiltonian of the Bose subsystem. The presence of the Fermi component leads to a qualitatively new behavior of the shift, as compared to the case of a single interacting Bose gas in the trap. Namely, the T _c(N) dependence has a different curvature in the presence of the Fermi component.     

The Heisenberg ferromagnet in spin coherent state representation

A new approach to Heisenberg ferromagnet using the spin coherent state representation is developed. The differential operator representation of spin angular momentum operators is used to derive thec-number analogs of the basic quantum mechanical equations, viz., the Schrödinger, Bloch and Liouville equations for the Heisenberg ferromagnet. As an important illustration of our formulation, which has noad hoc assumptions and does not use any boson representation, the excitation spectrum for one, two and three spin waves is obtained. In these cases it is also shown that eigenvalue spectrum can be obtained by completely ignoring the kinematical interactions.