Approximating parabolas as natural bounds of Heisenberg spectra: Reply on the comment of O. Waldmann

O. Waldmann has shown that some spin systems, which fulfill the condition of a weakly homogeneous coupling matrix, have a spectrum whose minimal or maximal energies are rather poorly approximated by a quadratic dependence on the total spin quantum number. We comment on this observation and provide the new argument that, under certain conditions, the approximating parabolas appear as natural bounds of the spectrum generated by spin coherent states.Comment: 2 pages, accepted for Europhysics Letter

Quantum rotational band model for the Heisenberg molecular magnet Mo72Fe30

We derive the low temperature properties of the molecular magnet Mo72Fe30, where 30 Fe(3+) paramagnetic ions occupy the sites of an icosidodecahedron and interact via isotropic nearest-neighbour antiferromagnetic Heisenberg exchange. The key idea of our model (J.S. & M.L.) is that the low-lying excitations form a sequence of rotational bands, i.e., for each such band the excitation energies depend quadratically on the total spin quantum number. For temperatures below 50 mK we predict that the magnetisation is described by a staircase with 75 equidistant steps as the magnetic field is increased up to a critical value and saturated for higher fields. For higher temperatures thermal broadening effects wash out the staircase and yield a linear ramp below the critical field, and this has been confirmed by our measurements (R.M.). We demonstrate that the lowest two rotational bands are separated by an energy gap of 0.7 meV, and this could be tested by EPR and inelastic neutron scattering measurements. We also predict the occurrence of resonances at temperatures below 0.1 K in the proton NMR spin-lattice relaxation rate associated with level crossings. As rotational bands characterize the spectra of many magnetic molecules our method opens a new road towards a description of their low-temperature behaviour which is not otherwise accessible.Comment: 7 pages, 6 figures, accepted for Europhysics Letter

Metamagnetic phase transition of the antiferromagnetic Heisenberg icosahedron

The observation of hysteresis effects in single molecule magnets like Mn$_{12}$-acetate has initiated ideas of future applications in storage technology. The appearance of a hysteresis loop in such compounds is an outcome of their magnetic anisotropy. In this Letter we report that magnetic hysteresis occurs in a spin system without any anisotropy, specifically, where spins mounted on the vertices of an icosahedron are coupled by antiferromagnetic isotropic nearest-neighbor Heisenberg interaction giving rise to geometric frustration. At T=0 this system undergoes a first order metamagnetic phase transition at a critical field \Bcrit between two distinct families of ground state configurations. The metastable phase of the system is characterized by a temperature and field dependent survival probability distribution.Comment: 4 pages, 4 figures, submitted to Physical Review Letter

Spin dynamics of quantum and classical Heisenberg dimers

Analytical solutions for the time-dependent autocorrelation function of the classical and quantum mechanical spin dimer with arbitrary spin are presented and compared. For large spin quantum numbers or high temperature the classical and the quantum dimer become more and more similar, yet with the major difference that the quantum autocorrelation function is periodic in time whereas the classical is not.Comment: 10 pages, 4 postscript figures, uses 'epsfig.sty'. Submitted to Physica A. More information available at http://www.physik.uni-osnabrueck.de/makrosysteme

Low temperature magnetization and the excitation spectrum of antiferromagnetic Heisenberg spin rings

Accurate results are obtained for the low temperature magnetization versus magnetic field of Heisenberg spin rings consisting of an even number N of intrinsic spins s = 1/2, 1, 3/2, 2, 5/2, 3, 7/2 with nearest-neighbor antiferromagnetic (AF) exchange by employing a numerically exact quantum Monte Carlo method. A straightforward analysis of this data, in particular the values of the level-crossing fields, provides accurate results for the lowest energy eigenvalue E(N,S,s) for each value of the total spin quantum number S. In particular, the results are substantially more accurate than those provided by the rotational band approximation. For s <= 5/2, data are presented for all even N <= 20, which are particularly relevant for experiments on finite magnetic rings. Furthermore, we find that for s > 1 the dependence of E(N,S,s) on s can be described by a scaling relation, and this relation is shown to hold well for ring sizes up to N = 80 for all intrinsic spins in the range 3/2 <= s <= 7/2. Considering ring sizes in the interval 8 <= N <= 50, we find that the energy gap between the ground state and the first excited state approaches zero proportional to 1/N^a, where a = 0.76 for s = 3/2 and a = 0.84 for s = 5/2. Finally, we demonstrate the usefulness of our present results for E(N,S,s) by examining the Fe12 ring-type magnetic molecule, leading to a new, more accurate estimate of the exchange constant for this system than has been obtained heretofore.Comment: Submitted to Physical Review B, 10 pages, 10 figure

Bounding and approximating parabolas for the spectrum of Heisenberg spin systems

We prove that for a wide class of quantum spin systems with isotropic Heisenberg coupling the energy eigenvalues which belong to a total spin quantum number S have upper and lower bounds depending at most quadratically on S. The only assumption adopted is that the mean coupling strength of any spin w.r.t. its neighbours is constant for all N spins. The coefficients of the bounding parabolas are given in terms of special eigenvalues of the N times N coupling matrix which are usually easily evaluated. In addition we show that the bounding parabolas, if properly shifted, provide very good approximations of the true boundaries of the spectrum. We present numerical examples of frustrated rings, a cube, and an icosahedron.Comment: 8 pages, 3 figures. Submitted to Europhysics Letter

Innate lymphoid cells and COVID-19 severity in SARS-CoV-2 infection

Background: Risk of severe COVID-19 increases with age, is greater in males, and is associated with lymphopenia, but not with higher burden of SARS-CoV-2. It is unknown whether effects of age and sex on abundance of specific lymphoid subsets explain these correlations. Methods: Multiple regression was used to determine the relationship between abundance of specific blood lymphoid cell types, age, sex, requirement for hospitalization, duration of hospitalization, and elevation of blood markers of systemic inflammation, in adults hospitalized for severe COVID-19 (n=40), treated for COVID-19 as outpatients (n=51), and in uninfected controls (n=86), as well as in children with COVID-19 (n=19), recovering from COVID-19 (n=14), MIS-C (n=11), recovering from MIS-C (n=7), and pediatric controls (n=17). Results: This observational study found that the abundance of innate lymphoid cells (ILCs) decreases more than 7-fold over the human lifespan - T cell subsets decrease less than 2-fold - and is lower in males than in females. After accounting for effects of age and sex, ILCs, but not T cells, were lower in adults hospitalized with COVID-19, independent of lymphopenia. Among SARS-CoV-2-infected adults, the abundance of ILCs, but not of T cells, correlated inversely with odds and duration of hospitalization, and with severity of inflammation. ILCs were also uniquely decreased in pediatric COVID-19 and the numbers of these cells did not recover during follow-up. In contrast, children with MIS-C had depletion of both ILCs and T cells, and both cell types increased during follow-up. In both pediatric COVID-19 and MIS-C, ILC abundance correlated inversely with inflammation. Blood ILC mRNA and phenotype tracked closely with ILCs from lung. Importantly, blood ILCs produced amphiregulin, a protein implicated in disease tolerance and tissue homeostasis. Among controls, the percentage of ILCs that produced amphiregulin was higher in females than in males, and people hospitalized with COVID-19 had a lower percentage of ILCs that produced amphiregulin than did controls. Conclusions: These results suggest that, by promoting disease tolerance, homeostatic ILCs decrease morbidity and mortality associated with SARS-CoV-2 infection, and that lower ILC abundance contributes to increased COVID-19 severity with age and in males. Funding: This work was supported in part by the Massachusetts Consortium for Pathogen Readiness and NIH grants R37AI147868, R01AI148784, F30HD100110, 5K08HL143183