Spectrum Of Elementary Excitations Research Articles

Magnetic Properties and Spin Kinetics of Two-Dimensional Heisenberg Antiferromagnets

In this report we present our study of two-dimensional Heisenberg magnets based on the picture of thermally excited skyrmions. The local order parameter, energy spectrum of elementary spin excitations above the skyrmion background, the skyrmion averaged radius and static magnetic susceptibility were obtained by the Green functions method. There was calculated the rate of nuclear relaxation caused by the interaction of nuclear spins with above mentioned spin excitations. The contribution of Moriya–Dsyloshinskii and anisotropic symmetric interactions into EPR line was considered. A comparison with NMR and neutron scattering experiments in cuprates and with the results obtained by other methods is given. We discuss the consequences of an interaction between skyrmions as the result of the spin fluctuations.

A computer investigation of a superfluid Bose liquid with pair interaction and with a coherent condensate of boson pairs as a model of 4He quantum liquid

One considers a superfluid (SF) state of a Bose liquid with repulsion between bosons, in which at T = 0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC), analogous to the Cooper condensate in a Fermi liquid with attraction between fermions. By iterations, one obtains a numerical solution of a closed system of nonlinear integral equations for the normal ∼ϵ 11 ( p , ω) and anomalous ∼ϵ 12( p, ω) self-energy parts in the framework of the model of “semi-transparent spheres”. A quasiparticle spectrum is then obtained, which is in good agreement with the experimental spectrum of elementary excitations in superfluid 4He.

Quantum topological excitations: from the sawtooth lattice to the Heisenberg chain

The recently elucidated structure of the delafossite YCuO$_{2.5}$ reveals a Cu-O network with nearly independent $\Delta$ chains having different interactions between the $s=1/2$ spins. Motivated by this result, we study the $\Delta$ chain for various ratios $J_{\rm bb}/J_{\rm bv}$ of the base-base and base-vertex interactions. By exact diagonalization and extrapolation, we show that the elementary excitation spectrum, which (within numerical error) is the same for total spins $S_{\rm tot}=0$ and 1, has a gap only in the interval $0.4874(1) \leq J_{\rm bb}/J_{\rm bv} \leq 1.53(1)$. The gap is dispersionless for $J_{\rm bb}/J_{\rm bv}=1$, but has increasing $k$-dependence as $J_{\rm bb}/J_{\rm bv}$ moves away from unity, related to the instability of dimers in the ground state.

Corrected Sum Rule, Generalized Virial Identity and Elementary Excitation Spectrum of Bose-Einstein Condensates at any Trapped Atom Number

Using a corrected sum rule and a generalized virial identity, we study the analytical expression for entire modes of the collective elementary excitation spectrum in a trapped Bose–Einstein condensate at any atom number. Explicit analytical formulas for the spectrum are obtained for the harmonic traps with both spherical symmetry and axial symmetry using the gaussian approximation for the N-body ground-state wave function of the condensate. These formulas give the simple dependence of all energy levels on the atom numbers, their interaction strength and trap geometry parameters.

A model of liquid flow in a channel with elastic walls

It is suggested to describe a liquid flow in a cylindrical round channel with elastic walls in terms of a two-fluid model used to describe the flow of He II in narrow capillaries near absolute zero. The idea is based on a similar (phonon-like) shape of the spectrum of elementary excitations at small wavenumbers k. The calculations show that the density ρn of a normal (i.e., viscous) liquid component (water in a steel tube) at 300 K is about 50 times smaller than the total density. This explains the paradox related to flow in a round tube for which anomalously large Reynolds numbers (Re∼105) are observed. Since Re∼ρn, real Reynolds numbers must also be about 50 times as small, that is, on the same order of magnitude as those for a flow between planes under otherwise equal conditions. A physical reason for the appearance of superfluidity at high (∼300 K) temperatures is a decrease in repulsion between small density fluctuations in the liquid, which is related to their interaction being screened by elastic waves in the channel walls.

The normal mode spectrum in a two-dimensional lattice of neutral atoms

The acoustic phonon spectrum in a two-dimensional lattice composed of neutral atoms is considered. It is demonstrated that the normal mode spectrum in a two-dimensional rectangular lattice cannot be obtained only with inclusion of the interaction between the nearest neighbors. The discrete equations describing normal modes are derived and analyzed. The possibility of forming the anisotropic spectra of elementary excitations is investigated for different parameters of the interatomic interaction potential. It is shown that the anisotropy of the phonon spectra in two-dimensional systems can manifest itself in different kinetic effects in which the electron-phonon interaction plays the decisive role.

Superfluid bose liquid with a suppressed BEC and an intensive pair coherent condensate as a model of 4He.

One introduces a model of the superfluid state of a Bose liquid with repulsion between bosons, in which at T=0, along with a weak single-particle Bose-Einstein condensate, there exists an intensive pair coherent condensate, analogous to the Cooper condensate in a Fermi liquid with attraction between fermions. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is solved numerically, and a quasiparticle spectrum is obtained, which is in good agreement with the experimental spectrum of elementary excitations in superfluid 4He. It is shown that the roton minimum in the spectrum is associated with the negative minimum of the Fourier component of the pair interaction potential.

Modification of superfluidity in a resonantly strongly driven Bose-Einstein condensate

We investigate the spectrum of elementary excitations for T=0 of a resonantly strongly driven two-component Bose-Einstein condensate (BEC) taking account of the Rabi oscillations. It is shown that the spectrum has two phononlike branches. Due to the inequality of the scattering lengths the Bogoliubov speed of sound of both branches differs from the Bogoliubov speed of sound for nondriven BEC, which leads to a modification of superfluidity. We have shown that the proposal to apply an additional resonant magnetic field in a scheme of the Feshbach resonance makes it possible to attain a very high sweep rate of the Feshbach resonance.

Self-consistent calculation of the spectrum of quasiparticles in a superfluid Bose liquid with a quenched Bose–Einstein condensate

An iterative method is used in a self-consistent calculation, at T=0, of the normal Σ11 and anomalous Σ12 self-energy parts, the boson polarization operator Π on the “mass shell,” and the quasiparticle spectrum E(p) in a superfluid Bose liquid with an interaction-quenched single-particle Bose–Einstein condensate (BEC). The calculation is based on a system of “truncated” integral equations for Σ11 and Σ12 with allowance for terms of first order in the density n0/n≪1 of the BEC and with the “bare” interaction between bosons taken in the form of the repulsive pseudopotential in the “semitransparent spheres” model, for which the Fourier component of the pseudopotential is an oscillatory sign-varying function of the momentum transfer. By fitting with a single adjustable parameter—the amplitude of the initial repulsive pseudopotential—one can achieve completely satisfactory agreement of the theoretical quasiparticle spectrum E(p) with the measured spectrum of elementary excitations in superfluid helium from neutron-scattering experiments over a wide momentum range (0⩽p⩽pmax≃4 Å−1).

Elementary electronic excitations in one-dimensional continuum and lattice systems

We systematically investigate the mode dispersion and spectral weight of the elementary excitation spectra in one-dimensional continuum and lattice electron systems by using the RPA, the Luttinger liquid model, and the Hubbard model. Both charge and spin excitations are studied in details and compared among the theoretical models. For the lattice Hubbard model we use both Bethe-ansatz equations and Lanczos-Gagliano method to calculate dispersion and spectral weight separately. We discuss the theoretically calculated elementary excitation spectra in terms of the experimental inelastic light (Raman) scattering spectroscopy of 1D semiconductor quantum wire systems. Our results show that in the polarized (i.e. non-spin-flip) Raman scattering spectroscopy, only the 1D charge density excitations should show up with observable spectral weight with the single particle excitations (in RPA) or singlet spin excitations (in the Luttinger model and the Hubbard model) having negligible spectral weight. The depolarized (spin-flip) Raman scattering spectra manifest the spin density or the triplet spin excitations. We also provide a qualitative comparison between the continuum and the lattice 1D elementary excitation spectra.

Dynamical probes of the elementary excitation spectrum for 2D spin models

Using the 2D Jordan–Wigner fermionization we calculate the zz dynamic structure factor of the s= 1 2 isotropic XY model on a spatially anisotropic square lattice. Within the frames of our approach S zz( k ,ω) is governed by a two-fermion excitation continuum. We discuss the modes ω k at which most of the spectral weight is concentrated or which form the boundaries of the continuum. We illustrate our findings considering in some detail the spatially isotropic case.

Perturbing a persistent current with an external potential

We consider the changes in the spectrum of elementary excitations of a flowing superfluid that result when a weak external perturbing potential is added. As a specific application, we study the critical velocity of superfluid flow in a slightly distorted, tight, toroidal trap for atoms. The critical velocity is not accurately predicted by the argument that the flow turns dissipative when the local flow velocity exceeds the local speed of sound somewhere in the fluid. The unusual critical velocity probably reflects the essentially one-dimensional physics of the model.

Structure of the superfluid component and spectrum of elementary excitations in the quantum Bose liquid He4

A self-consistent model is constructed for a superfluid Bose liquid in which the single-particle Bose–Einstein condensate (BEC) is suppressed on account of the strong interaction between bosons. The ratio of the density of the BEC to the total density of the Bose liquid is small, n0/n≪1, in contrast to the Bogolyubov theory for a nearly ideal Bose gas, in which the small parameter is the ratio of the number of overcondensate excitations to the number of particles in the intense BEC, (n−n0)/n0≪1. A closed system of nonlinear integral equations for the normal Σ̃11(p,ω) and anomalous Σ̃12(p,ω) self-energy parts is obtained in a renormalized perturbation theory constructed in the combined hydrodynamic (for p→0) and field (for p≠0) variables, the use of which ensures analyticity of the functions Σ̃ij(p,ε) for p→0 and ε→0 and a nonzero value of the superfluid order parameter Σ̃12(0,0)≠0 at T=0. It is shown that the structure of the quasiparticle spectrum E(p) and, in particular, the presence of a roton minimum are determined by the sign-varying and oscillatory behavior of the Fourier component of the pair interaction between bosons in the “hard spheres” model. An important role here is played by the renormalization (screening) of the pair interaction on account of many-particle (collective) effects, which are described by a polarization operator of the bosons on the “mass shell” and leads to enhancement of the effective attraction in certain regions of momentum space. It is shown that the superfluid component ρs at T→0 in this model is a superposition of the single-particle BEC and a pair coherent condensate, analogous to the condensate of Cooper pairs in superconductors. The structure of the superfluid state for T≠0 is also considered, with allowance for the appearance of a normal component ρn and a branch of second sound, the velocity of which goes to zero at the λ point. The applicability of the Landau superfluidity criterion is examined, and the question of the limiting permissible critical velocity of superfluid flow in the absence of quantum vortices is discussed.

Spin-1 antiferromagnetic Heisenberg chains in an external staggered field

We present in this paper a nonlinear \ensuremath{\sigma}-model analysis of a spin-1 antiferromagnetic Heisenberg chain in an external commensurate staggered magnetic field. After rediscussing briefly and extending previous results for the staggered magnetization curve, the core of the paper is a calculation at the tree level, of the Green functions of the model. We obtain precise results for the elementary excitation spectrum and in particular for the spin gaps in the transverse and longitudinal channels. It is shown that, while the spectral weight in the transverse channel is exhausted by a single magnon pole, in the longitudinal one, besides a magnon pole a two-magnon continuum appears as well whose weight is a steadily increasing function of the applied field, while the weight of the magnon decreases correspondingly. The balance between the two is governed by a sum rule that is derived and discussed. A detailed comparison with the present experimental and numerical state of the art as well as with previous analytical approaches is also made.

The combined effect of frustration and dimerizationin ferrimagnetic chains and square lattices

Within the zero-temperature linear spin-wave theory we haveinvestigated the effect of frustration and dimerization of aHeisenberg system with alternating spins s1 and s2 on one- andtwo-dimensional lattices. The combined effect appearsmost visibly in the elementary excitation spectra. In contrast to theground-state energy that decreases with dimerization and increaseswith frustration, the excitation energies are shown to be suppressedin energy by both dimerization and frustration. The excitationmodes also exhibit softening beyond a threshold value offrustration, signalling a transition from a classical ferrimagneticstate to a spiral state. The threshold value of frustration in achain decreases with dimerization, showing that dimerization furtherassists in the phase transition. That the long-range classicalferrimagnetic order is destroyed is shown by the correlation lengthas well as sublattice magnetization decreasing with bothdimerization and frustration. These effects have also been studiedfor a square lattice taking the dimerization interaction asJ/(1∓δ) rather than J(1±δ) where the linearspin-wave theory shows that dimerization initially opposes thefrustration-led transition to a spiral magnetic state, but thenhigher magnitudes of lattice deformation facilitate the transition.

Magnetic field effects on spin excitations in the spin-Peierls compoundCuGeO3

Neutron inelastic scattering measurements on an undoped single crystal of ${\mathrm{CuGeO}}_{3}$ and on a doped crystal ${\mathrm{CuGe}}_{0.997}{\mathrm{Si}}_{0.003}{\mathrm{O}}_{3}$ are performed in the presence of a magnetic field H up to 12 T. In the present work, a particular attention is given to the effect of H on the low-energy elementary excitations. This investigation is performed in the three different phases of the spin-Peierls system. In the dimerized D phase, the Zeeman splitting of the acoustic magnon branch is evaluated all along the dispersion branch $(0<q<~1/2).$ In the uniform U phase, it is established first that, at finite temperature $T\ensuremath{\ne}0,$ the low wave vector $(\stackrel{\ensuremath{\rightarrow}}{q}0)$ spinon modes are little affected by the thermal fluctuations $\ensuremath{\delta}{E}_{T}\ensuremath{\simeq}T.$ Second, the effect of H on the same low-$q$ mode results essentially in a transfer of the fluctuations towards the Zeeman-shifted lower boundary of the spinon continuum. Finally, our measurements on the doped compound establishes that an energy gap occurs in the elementary excitation spectrum of the incommensurate I phase.

Magnetoelastic coupling and long-range magnetic ordering in two-dimensional ferromagnets

In the present work the spectra of elementary excitations of a 2D easy-plane ferromagnet with the account of magnetoelastic coupling are investigated. It has been shown that the presence of magnetoelastic coupling results in the stabilization of long-range magnetic order. The Curie temperature has been evaluated.

4Electron self-trapping in intermediate-valentSmB6

SmB6 exhibits intermediate valence in the ground state and unusual behaviour at low temperatures. The resistivity and the Hall effect cannot be explained either by conventional sf-hybridization or by hopping transport in an impurity band. At least three different energy scales determine three temperature regimes of electron transport in this system. We consider the ground state properties, the soft valence fluctuations and the spectrum of band carriers in n-doped SmB6. The behaviour of excess conduction electrons in the presence of soft valence fluctuations and the origin of the three energy scales in the spectrum of elementary excitations is discussed. The carriers which determine the low-temperature transport in this system are self-trapped electron-polaron complexes rather than simply electrons in an impurity band. The mechanism of electron trapping is the interaction with soft valence fluctuations.

Microscopic Theory of Superfluid Helium

This paper discusses the properties of an interacting condensed Bose system, emphasizing those aspects which do not depend on the weakness of the potential, and which therefore apply to superfluid helium. A physical and mathematical characterization of Bose condensation is presented in terms of an additional macroscopic quantity, the wave function of the condensed mode, which is defined in terms of microscopic quantities. It is shown that in equilibrium the assumption of Bose condensation leads to a two-fluid model. The hydrodynamic generalization applicable to slowly varying disturbances from equilibrium is then discussed and rigorous microscopic expressions are derived for the parameters of this theory (including dissipative coefficients). The elementary excitation spectrum in this collision dominated regime is exhibited. The Landau quasi-particle theory is examined, as well as the relation of condensation and the excitation spectrum, to the property of superfluidity. Under certain regularity assumptions the form of the long-wavelength excitation spectrum at vanishing temperature is deduced. The corresponding derivation at finite temperature is presented and criticized. Finally, techniques are discussed for evaluating properties of the Bose system starting from the interaction potential. Approximation schemes consistent with the conservation laws and with the absence of a gap in the elementary excitation spectrum are discussed. Previous approximations for the weakly interacting Bose gas are classified and summarized and additional approximations are examined.

Attraction-repulsion transition between abrikosov vortices and Josephson vortices in the strongly layered superconductor Bi2Sr2CaCu2O8

A change in the effect of a frozen magnetic field parallel to the c-axis on rf power absorption, which is associated with the motion of Josephson vortices, is observed in the layered superconductor Bi2Sr2CaCu2O8 at a low temperature (∼15 K). The effect is interpreted as a change in the interaction between an Abrikosov vortex and a Josephson vortex from attraction (at high temperatures) to repulsion (at low temperatures). It is found that the dynamics of the magnetic flux parallel to the ab plane of the single crystal becomes irreversible upon a transition of the superconductor to the layered state. Possible reasons behind the observed effect are considered, one of them being a manifestation of the second superconducting transition in the elementary-excitation spectrum of a d-type superconductor near the core of Abrikosov vortices.