Mean-field theories for disordered electrons: Diffusion pole and Anderson localization

We discuss conditions to be put on mean-field-like theories to be able to describe fundamental physical phenomena in disordered electron systems. In particular, we investigate options for a consistent mean-field theory of electron localization and for a reliable description of transport properties. We argue that a mean-field theory for the Anderson localization transition must be electron-hole symmetric and self-consistent at the two-particle (vertex) level. We show that such a theory with local equations can be derived from the asymptotic limit to high spatial dimensions. The weight of the diffusion pole, i. e., the number of diffusive states at the Fermi energy, in this mean-field theory decreases with the increasing disorder strength and vanishes in the localized phase. Consequences of the disclosed behavior for our understanding of vanishing of electron diffusion are discussed.Comment: REVTeX4, 11 pages, no figure

Magnetic properties of a metal-organic antiferromagnet on a distorted honeycomb lattice

For temperatures T well above the ordering temperature T*=3.0+-0.2K the magnetic properties of the metal-organic material Mn[C10H6(OH)(COO)]2x2H20 built from Mn^2+ ions and 3-hydroxy-2-naphthoic anions can be described by a S=5/2 quantum antiferromagnet on a distorted honeycomb lattice with two different nearest neighbor exchange couplings J2 \approx 2J1 \approx 1.8K. Measurements of the magnetization M(H,T) as a function of a uniform external field H and of the uniform zero field susceptibility \chi(T) are explained within the framework of a modified spin-wave approach which takes into account the absence of a spontaneous staggered magnetization at finite temperatures.Comment: 11 pages, 11 figures; more thorough discussion of the dependence of the correlation length on the uniform magnetic field adde

Spin-wave interactions in quantum antiferromagnets

We study spin-wave interactions in quantum antiferromagnets by expressing the usual magnon annihilation and creation operators in terms of Hermitian field operators representing transverse staggered and ferromagnetic spin fluctuations. In this parameterization, which was anticipated by Anderson in 1952, the two-body interaction vertex between staggered spin fluctuations vanishes at long wavelengths. We derive a new effective action for the staggered fluctuations only by tracing out the ferromagnetic fluctuations. To one loop order, the renormalization group flow agrees with the nonlinear-$\sigma$-model approach.Comment: 7 pages, no figures; new references added; extended discussion on vertex structure. To appear in Europhysics Letter

Symplectic N and time reversal in frustrated magnetism

Identifying the time reversal symmetry of spins as a symplectic symmetry, we develop a large N approximation for quantum magnetism that embraces both antiferromagnetism and ferromagnetism. In SU(N), N>2, not all spins invert under time reversal, so we have introduced a new large N treatment which builds interactions exclusively out of the symplectic subgroup [SP(N)] of time reversing spins, a more stringent condition than the symplectic symmetry of previous SP(N) large N treatments. As a result, we obtain a mean field theory that incorporates the energy cost of frustrated bonds. When applied to the frustrated square lattice, the ferromagnetic bonds restore the frustration dependence of the critical spin in the Neel phase, and recover the correct frustration dependence of the finite temperature Ising transition.Comment: added reference

Spin Diffusion in Double-Exchange Manganites

The theoretical study of spin diffusion in double-exchange magnets by means of dynamical mean-field theory is presented. We demonstrate that the spin-diffusion coefficient becomes independent of the Hund's coupling JH in the range of parameters JH*S >> W >> T, W being the bandwidth, relevant to colossal magnetoresistive manganites in the metallic part of their phase diagram. Our study reveals a close correspondence as well as some counterintuitive differences between the results on Bethe and hypercubic lattices. Our results are in accord with neutron scattering data and with previous theoretical work for high temperatures.Comment: 4.0 pages, 3 figures, RevTeX 4, replaced with the published versio

Dyson-Maleev representation of nonlinear sigma-models

For nonlinear sigma-models in the unitary symmetry class, the non-linear target space can be parameterized with cubic polynomials. This choice of coordinates has been known previously as the Dyson-Maleev parameterization for spin systems, and we show that it can be applied to a wide range of sigma-models. The practical use of this parameterization includes simplification of diagrammatic calculations (in perturbative methods) and of algebraic manipulations (in non-perturbative approaches). We illustrate the use and specific issues of the Dyson-Maleev parameterization with three examples: the Keldysh sigma-model for time-dependent random Hamiltonians, the supersymmetric sigma-model for random matrices, and the supersymmetric transfer-matrix technique for quasi-one-dimensional disordered wires. We demonstrate that nonlinear sigma-models of unitary-like symmetry classes C and B/D also admit the Dyson-Maleev parameterization.Comment: 16 pages, 1 figur

Three dimensional generalization of the J1J_1-J2J_2 Heisenberg model on a square lattice and role of the interlayer coupling JcJ_c

A possibility to describe magnetism in the iron pnictide parent compounds in terms of the two-dimensional frustrated Heisenberg $J_1$-$J_2$ model has been actively discussed recently. However, recent neutron scattering data has shown that the pnictides have a relatively large spin wave dispersion in the direction perpendicular to the planes. This indicates that the third dimension is very important. Motivated by this observation we study the $J_1$-$J_2$-$J_c$ model that is the three dimensional generalization of the $J_1$-$J_2$ Heisenberg model for $S = 1/2$ and S = 1. Using self-consistent spin wave theory we present a detailed description of the staggered magnetization and magnetic excitations in the collinear state. We find that the introduction of the interlayer coupling $J_c$ suppresses the quantum fluctuations and strengthens the long range ordering. In the $J_1$-$J_2$-$J_c$ model, we find two qualitatively distinct scenarios for how the collinear phase becomes unstable upon increasing $J_1$. Either the magnetization or one of the spin wave velocities vanishes. For $S = 1/2$ renormalization due to quantum fluctuations is significantly stronger than for S=1, in particular close to the quantum phase transition. Our findings for the $J_1$-$J_2$-$J_c$ model are of general theoretical interest, however, the results show that it is unlikely that the model is relevant to undoped pnictides.Comment: 11 pages, 10 figures. Updated version, several references adde

Low-frequency noise in tunneling through a single spin

We propose measurements of low-frequency noise in the tunneling current through a single molecule with a spin as an experimental probe for identifying a mechanism of the spin-dependent tunneling. A specific tail near the zero frequency in the noise spectrum is predicted; the amplitude and the width of being of the same order of magnitude as the recently reported peak in the noise spectrum at the spin Larmor frequency. The ratio of the spectrum amplitudes at zero- and Larmor frequencies is shown to be a convenient tool for testing theoretical predictions.Comment: 4 pages, 3 figures. In the replaced version some mistakes are fixe

Quantum criticality of dipolar spin chains

We show that a chain of Heisenberg spins interacting with long-range dipolar forces in a magnetic field h perpendicular to the chain exhibits a quantum critical point belonging to the two-dimensional Ising universality class. Within linear spin-wave theory the magnon dispersion for small momenta k is [Delta^2 + v_k^2 k^2]^{1/2}, where Delta^2 \propto |h - h_c| and v_k^2 \propto |ln k|. For fields close to h_c linear spin-wave theory breaks down and we investigate the system using density-matrix and functional renormalization group methods. The Ginzburg regime where non-Gaussian fluctuations are important is found to be rather narrow on the ordered side of the transition, and very broad on the disordered side.Comment: 6 pages, 5 figure