Effective Hamiltonian in the Problem of a "Central Spin" Coupled to a Spin Environment

We consider here the problem of a "giant spin", with spin quantum number S>>1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes the low-energy properties of magnetic grains or magnetic macromolecules interacting with a surrounding spin environment, such as nuclear spins. We describe a general method for truncating the model to another one, valid at low energies, in which a two-level system interacts with the environmental spins, and higher energy terms are absorbed into a new set of couplings. This is done using an instanton technique. We then verify the accuracy of this technique, by comparing the results for the low energy effective Hamiltonian, with results derived for the original giant spin, coupled to a microscopic spin, using exact diagonalisation techniques.Comment: 15 pages, Latex, with 9 ps figure

Reply to the Comment on the 'Hole-digging' in ensembles of tunneling molecular magnets

Reply to the Comment of J.J. Alonso and J.F. Fernandez on the paper "'Hole-digging' in ensembles of tunneling molecular magnets" of I.S. Tupitsyn, P.C.E. Stamp and N.V. Prokof'ev (Phys. Rev. B 69, 132406, (2004)).Comment: 1 LaTeX page, 1 PS figure; submitted to PR

Landau Damping in an Electron Gas

Material science methods aim at developing efficient computational schemes for describing complex many-body effects and how they are revealed in experimentally measurable properties. Bethe-Salpeter equation in the self-consistent Hartree-Fock basis is often used for this purpose, and in this paper we employ the real-frequency diagrammatic Monte Carlo framework for solving the ladder-type Bethe-Salpeter equation for the 3-point vertex function (and, ultimately, for the system's polarization) to study the effect of electron-hole Coulomb scattering on Landau damping in the homogeneous electron gas. We establish how this damping mechanism depends on the Coulomb parameter $r_s$ and changes with temperature between the correlated liquid and thermal gas regimes. In a broader context of dielectric response in metals, we also present the full polarization and the typical dependence of the exchange-correlation kernel on frequency at finite momentum and temperature within the same computational framework.Comment: 5 pages and 4 figure

Solving the Bethe-Salpeter Equation in Real Frequencies at Finite Temperature

Self-consistent Hartree-Fock approximation combined with solutions of Bethe-Salpeter equation offers a powerful tool for studies of strong correlation effects arising in condensed matter models, nuclear physics, quantum field theories, and real materials. The standard finite-temperature approach would be to first solve the problem in the Matsubara representation and then apply numerical analytic continuation to the real-frequency axis to link theoretical results with experimental probes, but this ill-conditioned procedure often distorts important spectral features even for very accurate imaginary-frequency data. We demonstrate that the ladder-type finite-temperature Bethe-Salpeter equation in the Hartree-Fock basis for the 3-point vertex function and, ultimately, system's polarization can be accurately solved directly on the real frequency axis using the diagrammatic Monte Carlo technique and series resummation. We illustrate the method by applying it to the homogeneous electron gas model and demonstrate how multiple scattering events renormalize Landau damping.Comment: 5 pages 4 figure

Collective dynamics of interacting Ising spins: Exact results for the Bethe lattice

We study the low temperature dynamics in films made of molecular magnets, i. e. crystals composed of molecules having large electronic spin S in their ground state. The electronic spin dynamics is mediated by coupling to a nuclear spin bath; this coupling allows transitions for a small fraction of electronic spins between their two energy minima, Sz = ±S, under resonant conditions when the change of the Zeeman energy in magnetic dipolar field of other electronic spins is compensated by interaction with nuclear spins. Transitions of resonant spins can result in opening or closing resonances in their neighbors leading to the collective dynamics at sufficiently large density P0 of resonant spins. We formulate and solve the equivalent dynamic percolation problem for the Bethe lattice (BL) of spins interacting with z neighbors and find that depending on the density of resonant spins P0 and the number of neighbors z the system has either one (2 \u3c z \u3c 6) or two (z 6) kinetic transitions at P0 = Pc1 e-1/3/(3z) and P0 = Pc2 e-1/z. The former transition is continuous and associated with the formation of an infinite cluster of coupled resonant spins similarly to the static percolation transition occurring at P0 1/z. The latter transition, z \u3e 5, is discontinuous and associated with the instantaneous increase in the density of resonant spins from the small value 1/z to near unity. Experimental implications of our results are discussed

QED calculation of the 2p3/2-2p1/2 transition energy in five-electron ion of argon

We perform ab initio QED calculation of the (1s)^2(2s)^22p_{3/2} - (1s)^2(2s)^22p_{1/2} transition energy in the five-electron ion of argon. The calculation is carried out by perturbation theory starting with an effective screening potential approximation. Four different types of the screening potentials are considered. The rigorous QED calculations of the two lowest-order QED and electron-correlation effects are combined with approximate evaluations of the third- and higher-order electron-correlation contributions. The theoretical value for the wavelength obtained amounts to 441.261(70) (nm, air) and perfectly agrees with the experimental one, 441.2559(1) (nm, air).Comment: 10 pages, 3 figures, 1 tabl