High precision determination of the low-energy constants for the two-dimensional quantum Heisenberg model on the honeycomb lattice

The low-energy constants, namely the staggered magnetization density M? _s per spin, the spin stiffness ρ _s , and the spinwave velocity c of the two-dimensional (2-d) spin-1/2 Heisenberg model on the honeycomb lattice are calculated using first principles Monte Carlo method. The spinwave velocity c is determined first through the winding numbers squared. M? _s and ρ _s are then obtained by employing the relevant volume- and temperature-dependence predictions from magnon chiral perturbation theory. The periodic boundary conditions (PBCs) implemented in our simulations lead to a honeycomb lattice covering both a rectangular and a parallelogram-shaped region. Remarkably, by appropriately utilizing the predictions of magnon chiral perturbation theory, the numerical values of M? _s , ρ _s , and c we obtain for both the considered periodic honeycomb lattice of different geometries are consistent with each other quantitatively. The numerical accuracy reached here is greatly improved. Specifically, by simulating the 2-d quantum Heisenberg model on the periodic honeycomb lattice overlaying a rectangular area, we arrive at M? _s = 0.26882(3), ρ _s  = 0.1012(2)J, and c = 1.2905(8)Ja. The results we obtain provide a useful lesson for some studies such as simulating fermion actions on hyperdiamond lattice and investigating second order phase transitions with twisted boundary conditions.     

On the Absence of Ferromagnetism in Typical 2D Ferromagnets

We consider the Ising systems in d dimensions with nearest-neighbor ferromagnetic interactions and long-range repulsive (antiferromagnetic) interactions that decay with power s of the distance. The physical context of such models is discussed; primarily this is d = 2 and s = 3 where, at long distances, genuine magnetic interactions between genuine magnetic dipoles are of this form. We prove that when the power of decay lies above d and does not exceed d + 1, then for all temperatures the spontaneous magnetization is zero. In contrast, we also show that for powers exceeding d + 1 (with d ≥ 2) magnetic order can occur.     

Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems

Gapped ground states of quantum spin systems have been referred to in the physics literature as being ‘in the same phase’ if there exists a family of Hamiltonians H(s), with finite range interactions depending continuously on \({s\in [0,1]}\), such that for each s, H(s) has a non-vanishing gap above its ground state and with the two initial states being the ground states of H(0) and H(1), respectively. In this work, we give precise conditions under which any two gapped ground states of a given quantum spin system that ’belong to the same phase’ are automorphically equivalent and show that this equivalence can be implemented as a flow generated by an s-dependent interaction which decays faster than any power law (in fact, almost exponentially). The flow is constructed using Hastings’ ‘quasi-adiabatic evolution’ technique, of which we give a proof extended to infinite-dimensional Hilbert spaces. In addition, we derive a general result about the locality properties of the effect of perturbations of the dynamics for quantum systems with a quasi-local structure and prove that the flow, which we call the spectral flow, connecting the gapped ground states in the same phase, satisfies a Lieb-Robinson bound. As a result, we obtain that, in the thermodynamic limit, the spectral flow converges to a co-cycle of automorphisms of the algebra of quasi-local observables of the infinite spin system. This proves that the ground state phase structure is preserved along the curve of models H(s), 0 ≤ s ≤ 1.     

On the Dimension of the Singular Set of Solutions to the Navier–Stokes Equations

In this paper we prove that if a suitable weak solution u of the Navier–Stokes equations is an element of \({L^w(0,T;L^s(\mathbb{R}^3))}\), where 1 ≤ 2/w + 3/s ≤ 3/2 and 3 < w, s < ∞, then the box-counting dimension of the set of space-time singularities is no greater than max{w, s}(2/w + 3/s ? 1). We also show that if \({\nabla u \in L^w(0,T;L^s(\Omega))}\) with 2 < s ≤ w < ∞, then the Hausdorff dimension of the singular set is bounded by w(2/w + 3/s ? 2). In this way we link continuously the bounds on the dimension of the singular set that follow from the partial regularity theory of Caffarelli, Kohn, &; Nirenberg (Commun. Pure Appl. Math. 35:771–831, 1982) to the regularity conditions of Serrin (Arch. Ration. Mech. Anal. 9:187–191, 1962) and Beirão da Veiga (Chin. Ann. Math. Ser. B 16(4):407–412, 1995).     

Dependence of structure factor and correlation energy on the width of electron wires

The structure factor and correlation energy of a quantum wire of thickness b ? a _B are studied in random phase approximation (RPA) and for the less investigated region r _s < 1. Using the single-loop approximation, analytical expressions of the structure factor are obtained. The exact expressions for the exchange energy are also derived for a cylindrical and harmonic wire. The correlation energy in RPA is found to be represented by ? _c (b, r _s ) = α(r _s )/b + β(r _s ) ln(b) + η(r _s ), for small b and high densities. For a pragmatic width of the wire, the correlation energy is in agreement with the quantum Monte Carlo simulation data.     

A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity

We revisit and prove some convexity inequalities for trace functions conjectured in this paper’s antecedent. The main functional considered is

$ \Phi_{p,q} (A_1,\, A_2, \ldots, A_m) = \left({\rm Tr}\left[\left( \, {\sum\limits_{j=1}^m A_j^p } \, \right) ^{q/p} \right] \right)^{1/q} $

for m positive definite operators A _j . In our earlier paper, we only considered the case q = 1 and proved the concavity of Φ _p,1 for 0 < p ≤ 1 and the convexity for p = 2. We conjectured the convexity of Φ _p,1 for 1 < p < 2. Here we not only settle the unresolved case of joint convexity for 1 ≤ p ≤ 2, we are also able to include the parameter q ≥ 1 and still retain the convexity. Among other things this leads to a definition of an L ^q (L ^p ) norm for operators when 1 ≤ p ≤ 2 and a Minkowski inequality for operators on a tensor product of three Hilbert spaces – which leads to another proof of strong subadditivity of entropy. We also prove convexity/concavity properties of some other, related functionals.

     

Spin-precession-induced currents through ferromagnet/nanomagnet/superconductor junctions

The spin-precession-induced current through ferromagnet/nanomagnet/superconductorjunctions is investigated by using the nonequilibrium Green’s function method. It is foundthat the charge current I _c for the spinprecession frequency ω less than the energy gap Δ onlyarises from the equal-spin Andreev reflection, which is independent of the spinpolarization p of the ferromagnetic lead, while that forω > Δ mainly originates from the quasiparticle’scontribution. Both equal-spin AR and quasiparticle scattering processes contribute to thespin current I _s and the quasiparticlescattering process plays a dominant role. WhileI _c forω < Δ can be enhanced by the spin polarizationp, I _s decreases withp. These features may be of interest for ongoing experiments in thefield of molecular spintronics.     

Entropic Leggett–Garg inequality in neutrinos and <Emphasis Type="Italic">B</Emphasis>(<Emphasis Type="Italic">K</Emphasis>) meson systems

Entropic Leggett–Garg inequality is studied in systems like neutrinos in the context of two and three flavor neutrino oscillations and in neutral \(B_d\), \(B_s\) and K mesons. The neutrino dynamics is described with the matter effect taken into consideration. For the decohering B / K meson systems, the effect of decoherence and CP violation have also been taken into account, using the techniques of open quantum systems. Enhancement in the violation with increase in the number of measurements has been found, in consistency with findings in spin-s systems. The effect of decoherence is found to bring the deficit parameter \(\mathscr {D}^{[n]}\) closer to its classical value zero, as expected. The violation of entropic Leggett–Garg inequality lasts for a much longer time in K meson system than in \(B_d\) and \(B_s\) systems.     

Quantenstatistik eines Gases mit verschiedener Bahn- und Spintemperatur

A system of particles with spin in a magnetic field may possess an orbital temperatureT _o different from the spin temperatureT _s (?0), if it is possible to neglect the energetic interaction between the orbital and the spin system. The calculation of the quantum statistical most probable distribution of identical independent particles on the orbital and spin energy levels yields the introduction of three Lagrange multipliers—according to the fact that the orbital and the spin energy and the number of particles are fixed—representing the orbital and spin temperature and a generalizedPlanck's “characteristic function”. Apart from the Boltzmann-approximation being valid in the case of small spin values forT _o ?T _e (T _e =customary degeneration temperature) and arbitraryT _s ?0, the distributions and the orbital and the spin energy depend onboth the temperaturesT _o andT _s coming from the principle of exclusion forFermi resp.Bose particles. The equations of state are discussed. There are four heat capacities, which possess characteristic peaks. In stead of the well-known temperature independence of the paramagnetism of degenerated conducting electrons one obtains χ～T _o /T _s . The behaviour of the Einstein-condensation of aBose gas is considered.     

Duality-mediated critical amplitude ratios for the (2 + 1)-dimensional S = 1XY model

The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρ _s in the ordered phase and the vortex-condensate stiffness ρ _v in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios ρ _s,v /Δ (Δ: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρ _s /ρ _v admits a quantitative measure of deviation from selfduality.     

<Emphasis Type="Italic">g</Emphasis> factor of Li-like ions with a nonzero nuclear spin

A relativistic theory of the g factor of Li-like ions with a nonzero nuclear spin is considered for the 1s ² 2s state. A correction to the atomic g factor for the magnetic-dipole hyperfine interaction is calculated including the one-electron contribution, as well as the contribution of interelectronic-interaction effects of the order of 1/Z. Along with corrections for the interelectronic interaction, quantum electrodynamic effects, nuclear recoil, and finite nuclear size, this correction allows high-precision theoretical values for the g factor of Li-like ions with a nonzero nuclear spin to be obtained. The results can be used for refining the nuclear magnetic moments from comparison with experimentally determined values of the g factor.     

Das Kernquadrupolmoment des Mn55

With a recording photoelectric Fabry-Perot spectrometer and an atomic-beam light source the hyperfine structure of the Mn I-resonance linesλ=4031 Å,λ=4033 Å,λ=4034 Å (3d ⁵4s ² a ⁶ S _5/2?3d ⁵4s4p z ⁶ P _7/2,5/2,3/2 ⁰)and of the inter-combination linesλ=5395 Å andλ=5433 Å (3d ⁵4s ² a ⁶ S _5/2?3d ⁵4s4p z ⁸ P _7/2,5/2 ⁰) was measured. Furthermore the resonance lines have been measured with a pulsed atomic-beam in absorption. In this case the quotient (I ₀(ν)?I(ν))/I ₀(ν) was recorded, whereI(ν)=I ₀(ν) exp(?α(ν)d) is the observed intensity with absorption andI ₀(ν) the intensity of the light source. From the hyperfine structure splitting the value of the electric quadrupole moment of Mn⁵⁵ was derived to be:Q(Mn⁵⁵)=+(0.35±0.05)·10^?24 cm².     

Variable Temperature Single Crystal EPR Studies of Cu(II) in Dipotassium Diaquabis(Malonato-<Emphasis Type="Italic">κ</Emphasis><Superscript>2</Superscript><Emphasis Type="Italic">O,O</Emphasis>′) Nickelate Dihydrate: An Example of Contaminated Ground State

Single crystal X-band electron paramagnetic resonance (EPR) studies on divalent copper ions embedded in dipotassium diaquabis(malonato-κ ² O,O′) nickelate dihydrate have been performed at 300, 123 and 77 K to understand the nature of Jahn–Teller distortion in the paramagnetic host lattice. The angular variation of the EPR spectra reveals the presence of two sites, with one site not showing hyperfine resolution even at 77 K. The spin-Hamiltonian parameters of this six-coordinated Cu(II) ion, evaluated from EPR spectra at various temperatures, are:

• 300 K: g ₁₁ = 2.125, g ₂₂ = 2.118, g ₃₃ = 2.290, no copper hyperfine resolution
• 123 K: g ₁₁ = 2.229, g ₂₂ = 2.113, g ₃₃ = 2.319 and A ₁₁ = 5.02, A ₂₂ = 3.82, A ₃₃ = 6.87 mT
• 77 K: g ₁₁ = 2.224, g ₂₂ = 2.114, g ₃₃ = 2.324 and A ₁₁ = 5.32, A ₂₂ = 3.90, A ₃₃ = 7.06 mT

respectively. The low value observed for A ₃₃ at 123 and 77 K has been explained by assuming a ground state \({\text{d}}_{{x^{2} - y^{2} }}\) wave function for Cu(II) ions, contaminated with the excited state \({\text{d}}_{{z^{2} }}\). From the temperature dependence of the EPR spectra, the Cu(II) ions can be considered as a static Jahn–Teller system, with contaminated ground state. The admixture coefficients and bonding parameters have also been calculated by combining EPR and optical data. The EPR spectrum of powder sample confirms single crystal data.

     

The Boundary Control Approach to the Titchmarsh-Weyl <Emphasis Type="Italic">m</Emphasis>–Function. I. The Response Operator and the <Emphasis Type="Italic">A</Emphasis>–Amplitude

We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A?amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m?function associated with the Schrödinger operator H = ?? _x ²  + q(x) on L ₂(0, ∞) with Dirichlet boundary condition at x = 0.     

The signal photon flux,background photons and shot noise in electromagnetic response of high-frequency relic gravitational waves

On the basis of the electromagnetic response of high frequency relic gravitational waves (HFRGWs), we research on more accurate calculation of signal (i.e. transverse perturbative photon flux (PPF)) and background photons flux (BPF) in the sycro-resonance electromagnetic system, which consists of Gaussian beam (GB), a static magnetic field and fractal membranes. According to the relationship between frequency of gravitational waves and its dimensionless amplitude, we focus on the HFRGWs with ν _g  = 2.9 GHz, h ~ 10^?30 in the pre-big bang and quintessential inflationary models. The results show the peak value of the transverse BPF (~ 10²⁰ s^?1) is around |x| = 0.08 m, where |x| is the transverse distance to the longitudinal symmetrical surface of the GB, while the maximum transverse PPF always appears at x = 0 (\({N^{(1)}_{x} \sim 2.60\times10^{2}\,{\rm s}^{-1}}\) with the optimal phase difference between the GB and the resonant component of the HFRGWs δ = (n + 0.9)π, n = 0, 1, 2 . . .). However, the observable PPF should be ~ 1.19 × 10² s^?1 because of the stochastic nature of the HFRGWs’ phase. Since the decay speed of BPF is much quicker than PPF, it is hopeful to figure out the signal in some optimal regions. Moreover, we compare the decay speed of BPF and PPF in nature mode, and find the threshold value of x where PPF exceeds to BPF. It demonstrates that the limitation of our detection sensitivity comes from the strength of PPF rather than swamping by BPF. On the other hand, with the fractal membrane, the comparison between BPF and PPF provides the optimal detection area \({x\in[0.28,1]}\) m. In addition, through the calculation of shot noise and conservative estimation, we find that our sensitivity is h = 10^?26 in 4 months signal accumulate time.     

Ferrimagnetic nanoparticles for self-controlled magnetic hyperthermia

Based on the Heisenberg model including single-site uniaxial anisotropy and using aGreen’s function technique we studied the influence of size and composition effects on theCurie temperature T _C , saturationmagnetization M _S and coercivityH _C of spherical nanoparticles with astructural formulaM e _1?x Zn _x Fe₂O₄,Me = Ni, Cu, Co, Mn. It is shown that for x = 0.4–0.5and d = 10–20 nm these nanoparticles have aT _C  = 315 K and are suitable for aself-controlled magnetic hyperthermia.     

Positions of the magnetoroton minima in the fractional quantum Hall effect

The multitude of excitations of the fractional quantum Hall state are very accurately understood, microscopically, as excitations of composite fermions across their Landau-like Λ levels. In particular, the dispersion of the composite fermion exciton, which is the lowest energy spin conserving neutral excitation, displays filling-factor-specific minima called “magnetoroton” minima. Simon and Halperin employed the Chern-Simons field theory of composite fermions [Phys. Rev. B 48, 17368 (1993)] to predict the magnetoroton minima positions. Recently, Golkar et al. [Phys. Rev. Lett. 117, 216403 (2016)] have modeled the neutral excitations as deformations of the composite fermion Fermi sea, which results in a prediction for the positions of the magnetoroton minima. Using methods of the microscopic composite fermion theory we calculate the positions of the roton minima for filling factors up to 5/11 along the sequence s/ (2s + 1) and find them to be in reasonably good agreement with both the Chern-Simons field theory of composite fermions and Golkar et al.’s theory. We also find that the positions of the roton minima are insensitive to the microscopic interaction in agreement with Golkar et al.’s theory. As a byproduct of our calculations, we obtain the charge and neutral gaps for the fully spin polarized states along the sequence s/ (2s ± 1) in the lowest Landau level and the n = 1 Landau level of graphene.     

Über die Bestimmung des Spin-Abschneidekoeffizienten σ

A value ofσ=3, 5±1 is obtained for the spin cut off coefficient in the Fermi gas level density formula from a comparison of calculated and experimental (n, γ)-intensities feeding the observed levels of deformed nuclei in the rare earths region. The model used for the computations is tested at two nuclei with compound states of low spin (I _c =1/2) and high spin (I _c =13/2 or 15/2). The calculations can help to determine spins of nuclear levels in some cases.     

Niederenergetische Gammalinien vom Neutroneneinfang in Lu 175 und Lu 176

The low energy gamma-rays from neutron-capture in Lu 175 and Lu 176 have been investigated by means of the bent crystal-spectrometer at the DR-3-reactor at Risø. From the transitions in Lu 177 3 rotational bands have been determined. The levels of the (404)K=7/2⁺ groundstate rotational band are: 121,62 keV (I=9/2), 268,79keV (I=11/2), 440,66 keV (I=13/2), 636,22 keV (I=15/2), 854,34 keV (I=17/2). The level-sequence of the (514)K=9/2^?-band is: 150,39 keV (I=9/2), 288,99 keV (I=11/2), 451,49 keV (I=13/2), 637,05 keV (I=15/2) and 844,88 keV (I=17/2). At 457,92 keV is the basis for the (402)K=5/2⁺-band the higher levels of which are 552,05 keV (I=7/2), 671,89 keV (I=9/2), 816,63 keV (I=11/2), 985,23 keV (I=13/2), 1176,73keV (I=15/2) and probably 1389,5 keV (I=17/2). The energies of the levels apart from the 1389 keV-level have an accuracy of 7×10^?5. The energy differences between the 3 bands agree very well with the values expected from the Bohr-Mottelson-formulaE=A·I(I+1)+B·I ²(I+1)². The calculated branching-ratios within the 3 bands are in fairly good agreement with the experimental values. Theg _K -factors have been determined for 2 bands: It was found that for the (514)-bandg _K =1,16±0,04 and for the (402)-bandg _K =1,33±0,07.