International Journal of Modern Physics B

We present fundamental constraints required for a consistent linear response theory of fermionic superfluids and address temperatures both above and below the transition temperature T_c. We emphasize two independent constraints, one associated with gauge invariance (and the related Ward identity) and another associated with the compressibility sum rule, both of which are satisfied in strict BCS theory. However, we point out that it is the rare many body theory which satisfies both of these. Indeed, well studied quantum Hall systems and random-phase approximations to the electron gas are found to have difficulties with meeting these constraints. We summarize two distinct theoretical approaches which are, however, demonstrably compatible with gauge invariance and the compressibility sum rule. The first of these involves an extension of BCS theory to a mean field description of the BCS-Bose Einstein condensation crossover. The second is the simplest Nozieres Schmitt–Rink (NSR) treatment of pairing correlations in the normal state. As a point of comparison we focus on the compressibility κ of each and contrast the predictions above T_c. We note here that despite the compliance with sum rules, this NSR based scheme leads to an unphysical divergence in κ at the transition. Because of the delicacy of the various consistency requirements, the results of this paper suggest that avoiding this divergence may repair one problem while at the same time introducing others.

We consider the Heisenberg spin triangle with general coupling coefficients and general spin quantum number s. The corresponding classical system is completely integrable. In the quantum case the eigenvalue problem can be reduced to that of tridiagonal matrices in at most 2s+1 dimensions. The corresponding energy spectrum exhibits what we will call spectral symmetries due to the underlying permutational symmetry of the considered class of Hamiltonians. As an application we explicitly calculate six classes of universal polynomials that occur in the high temperature expansion of spin triangles and more general spin systems.

Measurement-induced nonlocality (MIN), introduced by Luo and Fu [Phys. Rev. Lett.106, 120401 (2011)], is a kind of quantum correlation which is different from entanglement and quantum discord (QD). MIN is defined over one-sided projective measurements. In this paper, we introduce a MIN over two-sided projective measurements. The nullity of this two-sided MIN is characterized, a formula for calculating two-sided MIN for pure states is proposed, and a lower bound of (two-sided) MIN for maximally entangled mixed states is given. In addition, we find that (two-sided) MIN is not continuous. Both finite- and infinite-dimensional cases are considered.

We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrödinger–Robertson inequality)? We find that the equality of the uncertainty relation cannot be reached for any two noncommuting observables, for finite dimensional Hilbert spaces if the Schmidt rank of the entangled state is maximal. One consequence is that the lower bound of the uncertainty relation can never be attained for any two observables for qubits, if the state is entangled. For infinite-dimensional Hilbert space too, we show that there is a class of physically interesting entangled states for which no two noncommuting observables can attain the minimum uncertainty equality.

We study the uniform solutions to the one-dimensional (1D) spinor Bose–Einstein condensates on a ring. These states explicitly display the associated motion of the super-current and the spin rotation, which give rise to fractional winding numbers according to the various compositions of the hyperfine states. It simultaneously yields a fractional factor to the global phase due to the spin-gauge symmetry. All fractional windings can be denoted as nk/(m+n), with nk<m+n<2F, for arbitrary spin-F Bose–Einstein condensation (BEC). Our method can be applied to explore the fractional vortices by identifying the ring as the boundary of two-dimensional (2D) spinor condensates.

We attempt to describe the magnetic properties of parent pnictide compounds by using both the J₁–J₂ Heisenberg model and its three-dimensional generalization, the J₁–J₂–J_c model. We also include spin anisotropy in the XY plane. In order to obtain the average magnetization and spin wave dispersion, we use the Green's functions method for spin operators in the random phase approximation. We obtain estimates for the model parameters by considering the low temperature experimental dispersion for the compounds CaFe₂As₂ and BaFe₂As₂ and conclude that theoretical dispersion can fit the experimental one if spatially anisotropic Hamiltonian is used. A good agreement between theory and experiment indicates that the Heisenberg model is applicable to parent pnictides at low temperatures. The applicability of the model for higher temperatures is checked by calculating the Néel temperature for both compounds. It turns out that the model overestimates the measured critical temperature. The Heisenberg model is not applicable to parent pnictides, for temperature comparable to Néel temperature. Our results thus confirm that all the magnetic properties of parent pnictides cannot be described with purely localized degrees of freedom, and that the itinerant magnetism should have an important role in these compounds. All results given in Sec. 3 are general and could be used in description of classes of compounds with spin stripe structure.

We analyze the full counting statistics (FCS) of a superconducting junction in nonequilibrium in the limit of small interface transparency. In this limit we treat both supercurrent and multiple Andreev reflections on equal footing and show how to generalize previous results for both phenomena. Furthermore, we also allow for different gaps of both superconductors and investigate the intermediate regime which allows to make contact with previous results on normal-superconductor heterostructures. We also compare our predictions in this regime to experimental data.

In this paper, we use the negativity and geometric quantum discord (GQD) to investigate the quantum phase transition (QPT) in the anisotropic spin-1/2 XY model with staggered Dzyaloshinskii–Moriya (DM) interaction using the quantum renormalization-group method, and the results show that the negativity and GQD can both obtain the quantum critical points associated with QPTs after several iterations of the renormalization. In addition to this, we discuss how the strength of the DM interaction and anisotropic parameter make the effect on the negativity and GQD for different RG steps. At last, we give out the relationship between negativity and GQD, and verify that with anisotropy parameter and the strength of DM interaction increased, the squared negativity and the normalization of GQD tend to equal in this model.

Based on a variable separated ODE method presented by Sirendaoreji and Sun, a modified variable separated ODE method is developed to uniformly construct the explicit exact solutions of sine-Gordon type equations by introducing a more general additional variable separated ODE. We demonstrate the effectiveness of our approach by applications to certain physically significant sine-Gordon type equations comprising the sine-Gordon equation and double sine-Gordon equation as particular examples. As a result, we cannot only recover the previously known exact solutions, but also pick up some new formal solutions for the sine-Gordon equation and double sine-Gordon equation by means of this approach.