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

Dipolar ground state of planar spins on triangular lattices

An infinite triangular lattice of classical dipolar spins is usually considered to have a ferromagnetic ground state. We examine the validity of this statement for finite lattices and in the limit of large lattices. We find that the ground state of rectangular arrays is strongly dependent on size and aspect ratio. Three results emerge that are significant for understanding the ground state properties: i) formation of domain walls is energetically favored for aspect ratios below a critical valu e; ii) the vortex state is always energetically favored in the thermodynamic limit of an infinite number of spins, but nevertheless such a configuration may not be observed even in very large lattices if the aspect ratio is large; iii) finite range approximations to actual dipole sums may not provide the correct ground sta te configuration because the ferromagnetic state is linearly unstable and the domain wall energy is negative for any finite range cutoff.Comment: Several short parts have been rewritten. Accepted for publication as a Rapid Communication in Phys. Rev.

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

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

Nonequilibrium orbital magnetization of strongly localized electrons

The magnetic response of strongly localized electrons to a time-dependent vector potential is considered. The orbital magnetic moment of the system, away from steady-state conditions, is obtained. The expression involves the tunneling and phonon-assisted hopping currents between localized states. The frequency and temperature dependence of the orbital magnetization is analyzed as function of the admittances connecting localized levels. It is shown that quantum interference of the localized wave functions contributes to the moment a term which follows adiabatically the time-dependent perturbation.Comment: RevTeX 3.

Spin-wave interaction in two-dimensional ferromagnets with dipolar forces

We discuss the spin-wave interaction in two-dimensional (2D) Heisenberg ferromagnet (FM) with dipolar forces at $T_C\gg T\ge0$ using 1/S expansion. A comprehensive analysis is carried out of the first 1/S corrections to the spin-wave spectrum. In particular, similar to 3D FM discussed in our previous paper A.V. Syromyatnikov, PRB {\bf 74}, 014435 (2006), we obtain that the spin-wave interaction leads to the {\it gap} in the spectrum $\epsilon_{\bf k}$ renormalizing greatly the bare gapless spectrum at small momenta $k$. Expressions for the spin-wave damping $\Gamma_{\bf k}$ are derived self-consistently and it is concluded that magnons are well-defined quasi-particles in both quantum and classical 2D FMs at small $T$. We observe thermal enhancement of both $\Gamma_{\bf k}$ and $\Gamma_{\bf k}/\epsilon_{\bf k}$ at small momenta. In particular, a peak appears in $\Gamma_{\bf k}$ and $\Gamma_{\bf k}/\epsilon_{\bf k}$ at small $k$ and at any given direction of $\bf k$. If $S\sim1$ the height of the peak in $\Gamma_{\bf k}/\epsilon_{\bf k}$ is not larger than a value proportional to $T/D\ll1$, where $D$ is the spin-wave stiffness. In the case of large spins $S\gg1$ the peak in $\Gamma_{\bf k}/\epsilon_{\bf k}$ cannot be greater than that of the classical 2D FM found at $k=0$ which height is small only {\it numerically}: $\Gamma_{\bf 0}/\epsilon_{\bf 0}\approx0.16$ for the simple square lattice. Frustrating next-nearest-neighbor exchange coupling increases $\Gamma_{\bf 0}/\epsilon_{\bf 0}$ in classical 2D FM only slightly. We find expressions for spin Green's functions and the magnetization. The latter differs from the well-known result by S.V. Maleev, Sov. Phys. JETP {\bf 43}, 1240 (1976). The effect of the exchange anisotropy is also discussed briefly

Two-dimensional quantum spin-1/2 Heisenberg model with competing interactions

We study the quantum spin-1/2 Heisenberg model in two dimensions, interacting through a nearest-neighbor antiferromagnetic exchange ($J$) and a ferromagnetic dipolar-like interaction ($J_d$), using double-time Green's function, decoupled within the random phase approximation (RPA). We obtain the dependence of $k_B T_c/J_d$ as a function of frustration parameter $\delta$, where $T_c$ is the ferromagnetic (F) transition temperature and $\delta$ is the ratio between the strengths of the exchange and dipolar interaction (i.e., $\delta = J/J_d$). The transition temperature between the F and paramagnetic phases decreases with $\delta$, as expected, but goes to zero at a finite value of this parameter, namely $\delta = \delta_c = \pi /8$. At T=0 (quantum phase transition), we analyze the critical parameter $\delta_c(p)$ for the general case of an exchange interaction in the form $J_{ij}=J_d/r_{ij}^{p}$, where ferromagnetic and antiferromagnetic phases are present.Comment: 4 pages, 1 figur

Quantum Field Theory for the Three-Body Constrained Lattice Bose Gas -- Part I: Formal Developments

We develop a quantum field theoretical framework to analytically study the three-body constrained Bose-Hubbard model beyond mean field and non-interacting spin wave approximations. It is based on an exact mapping of the constrained model to a theory with two coupled bosonic degrees of freedom with polynomial interactions, which have a natural interpretation as single particles and two-particle states. The procedure can be seen as a proper quantization of the Gutzwiller mean field theory. The theory is conveniently evaluated in the framework of the quantum effective action, for which the usual symmetry principles are now supplemented with a ``constraint principle'' operative on short distances. We test the theory via investigation of scattering properties of few particles in the limit of vanishing density, and we address the complementary problem in the limit of maximum filling, where the low lying excitations are holes and di-holes on top of the constraint induced insulator. This is the first of a sequence of two papers. The application of the formalism to the many-body problem, which can be realized with atoms in optical lattices with strong three-body loss, is performed in a related work [14].Comment: 21 pages, 5 figure

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