Baxter operators with deformed symmetry

Baxter operators are constructed for quantum spin chains with deformed _s?2${\mathrm{s?}}_2$ symmetry. The parallel treatment of Yang–Baxter operators for the cases of undeformed, trigonometrically and elliptically deformed symmetries presented earlier and relying on the factorization regarding parameter permutations is extended to the global chain operators following the scheme worked out recently in the undeformed case.     

Cyclic calorons

The Nahm data of periodic instantons, often called calorons, with spatial _CN$C_N$-symmetries are considered, by applying Sutcliffe?s ansatz for the monopoles with _CN$C_N$-symmetries. The bulk data of calorons are shown to enjoy the periodic Toda lattice, and the solutions are given in terms of elliptic theta functions. The case of N=3$N=3$ calorons are investigated in detail. It is found that the “scale parameters” of these calorons have upper bounds in their values, so that they do not have the large scale, or monopole, limits. The instanton limit of the _C3$C_3$-symmetric caloron is obtained.     

Spin fluctuations and unconventional pairing on the Lieb lattice

The spin fluctuations and superconducting pairing symmetries in the dispersive band of Lieb lattice are studied by fluctuation exchange approximation. The antiferromagnetic spin density wave is found to exist on the A sublattice (the lattice sites with four nearest neighbors) at half filling. When slightly doped away from half filling, a balance between the combined effects of the (π,π$\pi ,\pi$) and (0.4π,0$0.4\pi ,0$) spin fluctuations and the gaining of the condensation energy leads to the nearly degenerate _dx2−y2$d_{x^2-y^2}$- and _gxy(x2−y2)$g_{xy(x^2-y^2)}$-wave pairing states. After further doped, the _dxy$d_{xy}$-wave state is favored via the intra-sublattice spin fluctuations with a wave vector (π,0$\pi ,0$). We emphasize that the sublattices' contribution and the renormalization of the spectral function play a crucial role on the spin fluctuations and the pairing symmetry. The effect of the imbalance of the on-site energy at different sublattices is also discussed.     

Theory of twist liquids: Gauging an anyonic symmetry

Topological phases in (2+1)$(2+1)$-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric–magnetic duality, that relabel anyons without affecting the topological structures. Twist defects are static point-like objects that permute the labels of orbiting anyons. Gauging these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases referred as twist liquids  , which are generically non-Abelian. We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions. We explicitly demonstrate the gauging of the Z₂${\mathbb{Z}}_2$-symmetric toric code, SO(2N)₁$SO{\left(2N\right)}_1$ and SU(3)₁$SU{\left(3\right)}_1$ state as well as the S₃$S_3$-symmetric SO(8)₁$SO{\left(8\right)}_1$ state and a non-Abelian chiral state we call the “4-Potts” state.     

Entanglement thresholds for displaying the quantum nature of teleportation

A protocol for transferring an unknown single qubit state evidences quantum features when the average fidelity of the outcomes is, in principle, greater than 2/3$2/3$. We propose to use the probabilistic and unambiguous state extraction scheme   as a mechanism to redistribute the fidelity in the outcome of the standard teleportation when the process is performed with an X$X$-state as a noisy quantum channel. We show that the entanglement of the channel is necessary but not sufficient in order for the average fidelity f_X$f_X$ to display quantum features, i.e., we find a threshold C_X$C_X$ for the concurrence of the channel. On the other hand, if the mechanism for redistributing fidelity is successful then we find a filterable outcome with average fidelity f_X,0$f_{X,0}$ that can be greater than f_X$f_X$. In addition, we find the threshold concurrence of the channel C_X,0$C_{X,0}$ in order for the average fidelity f_X,0$f_{X,0}$ to display quantum features and surprisingly, the threshold concurrence C_X,0$C_{X,0}$ can be less than C_X$C_X$. Even more, we find some special cases for which the threshold values become zero.     

Real hypersurfaces in complex two-plane Grassmannians with commuting Ricci tensor

In this paper, first we introduce the full expression for the Ricci tensor of a real hypersurface M$M$ in complex two-plane Grassmannians _G2(C^m+2)$G_2\left({\mathbb{C}}^{m+2}\right)$ from the equation of Gauss. Next we prove that a Hopf hypersurface in complex two-plane Grassmannians _G2(C^m+2)$G_2\left({\mathbb{C}}^{m+2}\right)$ with commuting Ricci tensor is locally congruent to a tube of radius r$r$ over a totally geodesic _G2(C^m+1)$G_2\left({\mathbb{C}}^{m+1}\right)$. Finally it can be verified that there do not exist any Hopf Einstein hypersurfaces in _G2(C^m+2)$G_2\left({\mathbb{C}}^{m+2}\right)$.     

Influences of DMI on spin-polarized current through a single-molecule magnet

We theoretically investigate the influences of the Dzyaloshinskii–Moriya interaction (DMI) on the spin-polarized transport through a single-molecular magnets, which is weakly coupled to ferromagnetic lead-L(_pL)$\mathrm{L}(p_L)$ and nonmagnetic lead-R. The spin current is obtained by means of the rate-equation approach in the sequential-tunneling region. Due to the coherent superposition of the molecular state |1,m〉^±${|1,m〉}^{\pm }$ induced by the DMI, we can observe the continuous pure spin current and negative differential conductance (NDC) under the full polarization _pL=1$p_L=1$ condition and polarization reversal of spin-current in the case of 0<_pL<1$0<p_L<1$. These novel phenomena may be useful in the development of molecular spintronics devices.     

A model with two inert scalar doublets

We consider an extension of the standard model (SM) with three SU(2)$SU\left(2\right)$ scalar doublets and discrete S₃⊗Z₂$S_3\otimes {\mathbb{Z}}_2$ symmetries. The irreducible representation of S₃$S_3$ has a singlet and a doublet, and here we show that the singlet corresponds to the SM-like Higgs and the two additional SU(2)$SU\left(2\right)$ doublets forming a S₃$S_3$ doublet are inert. In general, in a three scalar doublet model, with or without S₃$S_3$ symmetry, the diagonalization of the mass matrices implies arbitrary unitary matrices. However, we show that in our model these matrices are of the tri-bimaximal type. We also analyzed the scalar mass spectra and the conditions for the scalar potential is bounded from below at the tree level. We also discuss some phenomenological consequences of the model.     

The Haldane–Shastry spin chain and the topological basis realization

In this paper, based on the topological basis states, we investigate the Hamiltonian family {H₂,H₃,H₄}$\{H_2,H_3,H_4\}$ of a closed four-qubit Haldane–Shastry spin chain. Not only the two-qubit interaction form, but also the three-qubit interaction form and the four-qubit interaction form are presented in terms of spin operators. Meanwhile, we explore some particular properties of the topological basis states in these systems. With Yangian algebra, the symmetry of the systems and the transitions between the eigenstates have been investigated. We find a really useful effect of Y(sl(2))$Y\left(sl\left(2\right)\right)$ operators {J_±,J₃}$\{J_{\pm },J_3\}$, which is that they can describe the transitions between the spin single state and the spin triple states. Furthermore, we construct a new Hamiltonian, whose energy degeneracies can be changed by adjusting the strengths of the two-qubit interactions, three-qubit interactions, four-qubit interactions, and the external magnetic field.     

Shot noise in HTc superconductor quantum point contact system

We study the electrical transport properties of a quantum point contact between a lead and a high Tc superconductor. For this, we use the Hamiltonian approach and non-equilibrium Green functions of the system. The electrical current and the shot noise are calculated with this formalism. We consider d_x²−y²${\mathrm{d}}_{x^2-y^2}$, d_xy${\mathrm{d}}_{\mathit{xy}}$, d_x²−y²+is${\mathrm{d}}_{x^2-y^2}+\mathrm{is}$ and d_xy+is${\mathrm{d}}_{\mathit{xy}}+\mathrm{is}$ symmetries for the pair potential. Also we explore the s₊₋${\mathrm{s}}_{+-}$ and s₊₊${\mathrm{s}}_{++}$ symmetries describing the behavior of the ferropnictides superconductors. We found that for d_xy${\mathrm{d}}_{\mathit{xy}}$ symmetry there is not a zero bias conductance peak and for d+is$\mathrm{d}+\mathrm{is}$ symmetries there is a displacement of the transport properties. From shot noise and current, the Fano factor is calculated and we found that it takes values of effective charge between e and 2e  , this is explained by the diffraction of quasiparticles in the contact. For the s₊₋${\mathrm{s}}_{+-}$ and s₊₊${\mathrm{s}}_{++}$ symmetries the results show that the electrical current and the shot noise depend on the mixing coefficient, furthermore, the effective electric charge can take values between 0 and 2e, in contrast with the results obtained for s wave superconductors.     

Thermodynamics properties of an anisotropic Ising antiferromagnet in both external longitudinal and transverse fields

We have studied the anisotropic two-dimensional nearest-neighbor Ising model with competitive interactions in both uniform longitudinal field H$H$ and transverse magnetic field Ω$\Omega$. Using the effective-field theory (EFT) with correlation in cluster with N=1$N=1$ spin we calculate the thermodynamic properties as a function of temperature with values H$H$ and Ω$\Omega$ fixed. The model consists of ferromagnetic interaction _Jx$J_x$ in the x$x$ direction and antiferromagnetic interaction _Jy$J_y$ in the y$y$ direction, and it is found that for H/_Jy∈[0,2]$H/J_y\in [0,2]$ the system exhibits a second-order phase transition. The thermodynamic properties are obtained for the particular case of λ=_Jx/_Jy=1$\lambda =J_x/J_y=1$ (isotropic square lattice).     

Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.     

First-principles materials design of CuInSe2-based high-efficiency photovoltaic solar cells

Based on ab initio   electronic structure calculations by self-interaction-corrected local-density-approximation (SIC-LDA) with the Korringa–Kohn–Rostoker coherent potential approximation (KKR-CPA), we propose a materials design for high efficiency photovoltaic solar cells (PVSCs). It is shown that (i) the concentration dependence of the mixing energy of CuIn_1−xGa_xSe₂${\mathrm{CuIn}}_{1-x}{\mathrm{Ga}}_x{\mathrm{Se}}_2$ shows upward convexity, thus this system favors phase separation. Due to the type II band alignment between CuInSe₂${\mathrm{CuInSe}}_2$ and CuGaSe₂${\mathrm{CuGaSe}}_2$, efficient electron–hole separation is realized in decomposed phase of this system. (ii) CuIn_1−xZn_0.5xSn_0.5xSe₂${\mathrm{CuIn}}_{1-x}{\mathrm{Zn}}_{0.5x}{\mathrm{Sn}}_{0.5x}{\mathrm{Se}}_2$ has a direct band gap and no impurity state appears in the gap. Therefore, cost reduction is possible by using Zn and Sn instead of In. (iii) n-type CuAl_1−xSn_xS₂${\mathrm{CuAl}}_{1-x}{\mathrm{Sn}}_x{\mathrm{S}}_2$ and p-type Cu_1−xV_CuxAlS₂${\mathrm{Cu}}_{1-x}{\mathrm{V}}_{\mathrm{Cu}x}{\mathrm{AlS}}_2$ have negative activation energy for doped impurities and are expected to be low-resistive transparent conducting sulfides, which should be useful for CuInSe₂${\mathrm{CuInSe}}_2$-based PVSCs.     

Deterministic LOCC transformation of three-qubit pure states and entanglement transfer

A necessary and sufficient condition of the possibility of a deterministic local operations and classical communication (LOCC) transformation of three-qubit pure states is given. The condition shows that the three-qubit pure states are a partially ordered set parametrized by five well-known entanglement parameters and a novel parameter; the five are the concurrences C_AB$C_{AB}$, C_AC$C_{AC}$, C_BC$C_{BC}$, the tangle τ_ABC${\tau }_{ABC}$ and the fifth parameter J₅$J_5$ of Acín et al. (2000) Ref. [19], while the other new one is the entanglement charge Q_e$Q_{\text{e}}$. The order of the partially ordered set is defined by the possibility of a deterministic LOCC transformation from a state to another state. In this sense, the present condition is an extension of Nielsen’s work (Nielsen (1999) [14]) to three-qubit pure states. We also clarify the rules of transfer and dissipation of the entanglement which is caused by deterministic LOCC transformations. Moreover, the minimum number of times of measurements to reproduce an arbitrary deterministic LOCC transformation between three-qubit pure states is given.     

Generalized Einstein real hypersurfaces in complex two-plane Grassmannians

In this paper we give a complete classification of pseudo-Einstein real hypersurfaces in complex two-plane Grassmannians _G2(C^m+2)$G_2\left({\mathbb{C}}^{m+2}\right)$. As an application of this result we prove that there do not exist Einstein Hopf or D^⊥${\mathfrak{D}}^{\perp }$-invariant Einstein real hypersurfaces in _G2(C^m+2)$G_2\left({\mathbb{C}}^{m+2}\right)$.     

Piezoelectric resonance in Rochelle salt: The contribution of diagonal strains

Within the framework of two-sublattice Mitsui model with taking into account the shear strain ε₄${\epsilon }_4$ and the diagonal strains ε₂${\epsilon }_2$ and ε₃${\epsilon }_3$, a dynamic dielectric response of Rochelle salt X-cuts is considered. Experimentally observed phenomena of crystal clamping by high frequency electric field, piezoelectric resonance, and microwave dispersion are described. Analytical expressions for the resonant frequencies of these cuts, associated with the shear vibration mode of ε₄${\epsilon }_4$ and with the extensional in-plane modes of ε₂${\epsilon }_2$, ε₃${\epsilon }_3$, are derived. It is shown that the lowest resonant frequency is always associated with the ε₄${\epsilon }_4$ shear mode.     

On partition function and Weyl anomaly of conformal higher-spin fields

We study 4-dimensional higher-derivative conformal higher-spin (CHS) fields generalizing Weyl graviton and conformal gravitino. They appear, in particular, as “induced” theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. Remarkably, the bosonic (integer spin s) CHS partition function appears to be given by a product of partition functions of the standard 2nd-derivative “partially massless” spin s   fields, generalizing the previously known expression for the 1-loop Weyl graviton (s=2$s=2$) partition function. We compute the corresponding spin s   Weyl anomaly coefficients _as${\mathrm{a}}_s$ and _cs${\mathrm{c}}_s$. Our result for _as${\mathrm{a}}_s$ reproduces the expression found recently in arXiv:1306.5242 by an indirect method implied by AdS/CFT (which relates the partition function of a CHS field on S⁴$S^4$ to a ratio of known partition functions of massless higher-spin field in AdS₅ with alternate boundary conditions). We also obtain similar results for the fermionic CHS fields. In the half-integer s case the CHS partition function on (A)dS background is given by the product of squares of “partially massless” spin s partition functions and one extra factor corresponding to a special massive conformally invariant spin s field. It was noticed in arXiv:1306.5242 that the sum of the bosonic _as${\mathrm{a}}_s$ coefficients over all s is zero when computed using the ζ-function regularization, and we observe that the same property is true also in the fermionic case.     

Comparative kinetic stability of classical and non-classical fullerenes C46

Molecular dynamics is used to study the kinetic stability of a classical fullerene C₄₆ and its non-classical analog with a square. The lifetimes of both clusters till the moments of their isomerization are directly calculated as functions of temperature. The activation energies _Ea$E_a$ of isomerization processes are determined from the fits of the results obtained to the Arrhenius law. For the non-classical fullerene, the value of _Ea=3.1±0.2 eV$E_a=3.1\pm 0.2\text{eV}$ is found to be considerably below that for the classical one, _Ea=4.5±0.3 eV$E_a=4.5\pm 0.3\text{eV}$. In view of rather low kinetic stability of non-classical C₄₆, its experimental registration in a gas phase seems to be problematic.