3,378 research outputs found
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--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 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
renormalizing greatly the bare gapless spectrum at small momenta .
Expressions for the spin-wave damping are derived
self-consistently and it is concluded that magnons are well-defined
quasi-particles in both quantum and classical 2D FMs at small . We observe
thermal enhancement of both and at small momenta. In particular, a peak appears in and
at small and at any given direction of
. If the height of the peak in is not larger than a value proportional to , where is the
spin-wave stiffness. In the case of large spins the peak in
cannot be greater than that of the classical
2D FM found at which height is small only {\it numerically}: for the simple square lattice. Frustrating
next-nearest-neighbor exchange coupling increases 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 () and a ferromagnetic
dipolar-like interaction (), using double-time Green's function, decoupled
within the random phase approximation (RPA). We obtain the dependence of as a function of frustration parameter , where is the
ferromagnetic (F) transition temperature and is the ratio between the
strengths of the exchange and dipolar interaction (i.e., ). The
transition temperature between the F and paramagnetic phases decreases with
, as expected, but goes to zero at a finite value of this parameter,
namely . At T=0 (quantum phase transition), we
analyze the critical parameter for the general case of an
exchange interaction in the form , 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 - Heisenberg model on a square lattice and role of the interlayer coupling
A possibility to describe magnetism in the iron pnictide parent compounds in
terms of the two-dimensional frustrated Heisenberg - 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 --
model that is the three dimensional generalization of the -
Heisenberg model for 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 suppresses the quantum fluctuations and
strengthens the long range ordering. In the -- model, we find
two qualitatively distinct scenarios for how the collinear phase becomes
unstable upon increasing . Either the magnetization or one of the spin
wave velocities vanishes. For renormalization due to quantum
fluctuations is significantly stronger than for S=1, in particular close to the
quantum phase transition. Our findings for the -- 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
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