The exact ground state and the origin of the spin gap in the distorted mixed spin (1, 1/2) diamond chain

By using the method of exact diagonalization, we investigated the properties of the distorted mixed spin (1, 1/2) diamond chain with antiferromagnetic interactions along the rung and leg. The ground states of this model contain the sawtooth chain state and the rung dimer plus Haldane state. The research on the origin of the spin gap of the model discloses that there are three different types of spin excitations at different parameter regimes due to the competition among the interactions J₁, J₂ and J₃.     

Microwave spectrum of silyl fluoride: Coriolis resonance between ν2 and ν5 states

The J = 1 ← 0 and J = 2 ← 1 microwave rotational transitions of SiH₃F and SiD₃F have been measured for the ground and the v₂ = 1, v₃ = 1, v₅ = 1, and v₆ = 1 vibrational states, for which the various rotational and vibration-rotation interaction constants have been obtained. Both molecules show an X-Y Coriolis resonance between the ν₂ and ν₅ vibrational states, whose separation are 29 and 8 cm^?1, respectively. In the case of SiD₃F the resonance is very strong and an exact numerical diagonalization of the energy matrix was employed.     

Spin-correlations and low lying excited states of the spin-1/2 Heisenberg antiferromagnet on a square lattice

The ground state and the lowest excited states of the spin 1/2-Heisenberg model are investigated by exact diagonalization and variational Monte Carlo techniques. Our trial state represents a generalization of a wave function introduced by Hulthen, Kasteleijn and Marshall. The long range character of the spin-correlation function is in excellent agreement with exact diagonalization and also with recent neutron scattering results for La₂CuO₄. The asymptotic behavior of the spin-correlation function is found to differ from spin-wave theory. From the exact (N<=20 spins) and variational (N<=400) ground state energies we determine as asymptotic values 1.3025 and 1.288, respectively. We calculate the dispersion for the spin-wave excitations and identify an excited triplet which becomes degenerate with the ground state in the thermodynamic limit. This triplet state allows spontaneous symmetry breaking to occur atT=0 K. Quantum fluctuations reduce the sublattice magnetization to an effective value of 0.195 (3) as compared to the Néel-state value of 1/2.     

Collective excitations in the 1-D-ferromagnet CsFeCl3 with singlet ground state

By means of inalastic neutron scattering we have determined the dispersion relation of the magnetic excitations in CsFeCl₃ at different temperatures.The dispersion in c-direction, along the Fe-chains is typically ferromagnetic and in the hexagonal plane antiferromagnetic. Due to the lack of an applicable theory the data were parametrized by the simple heuristic formula:?ω = [2J[1 - cos πq_c] [A + 2J(1 - cos π)q_c)] + [C + J' (1.5 + γ(q))]²]^{$\text{1}\text{2}$}The gap was found to be C = 0.148 THz, the easy plane anisotropy A = 0.308 THz, the ferromagnetic interaction J = 0.148 THz and the antiferromagnetic interaction J' = -0.04 THz. At 1.25 K all excitations had a width smaller than the instrumental resolution ΔE = 0.025 THz. These results can be interpreted as follows: CsFeCl₃ is a singlet ground state system with strong ferromagnetic interaction J along the crystallographic c-axis and weak antiferromagnetic interaction J' in the plane perpendicular to c.In addition we have measured the influence of a magnetic field along the hexagonal c-axis. The splitting found agrees with the assumed level scheme yielding g = 2.5 for the first excited level.     

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

From the recently determined structure of the delafossite YCuO_2.5, we argue that the Cu-O network has nearly independent Δ chains but with different interactions between the s = 1/2 spins. Motivated by this observation, we study the Δ chain for different ratios of the base-base and base-vertex interactions, J _bb/J _bv. By exact diagonalization and extrapolation, we show that the elementary excitation spectrum is the same for total spins S _tot = 0 and 1, but not for S _tot = 2, and has a gap only in the interval 0.4874(1) ⩽ J _bb/J _bv ⩽ 1.53(1). The gap, known to be dispersionless for J _bb = J _bv, is found to acquire increasing k-dependence as J _bb/J _bv moves away from unity. Received 29 October 2002 / Received in final form 14 January 2003 Published online 6 March 2003 RID="a" ID="a"e-mail: sblundell@cea.fr RID="b" ID="b"e-mail: nunezreg@lps.u-psud.fr     

Jordan-Wigner approach to the frustrated spin one-half XXZ chain

The Jordan-Wigner transformation is applied to study the ground state properties and dimerization transition in the J₁-J₂ XXZ chain. We consider different solutions of the mean-field approximation for the transformed Hamiltonian. Ground state energy and the static structure factor are compared with complementary exact diagonalization and good agreement is found near the limit of the Majumdar-Ghosh model. Furthermore, the ground state phase diagram is discussed within the mean-field theory. In particular, we show that an incommensurate ground state is absent for large J₂ in a fully self-consistent mean-field analysis.     

Millimeter wave spectrum of acetonitrile oxide,CH3CNO,in the ν10 vibrational manifold: The ground state and the state v10 = 1

The pure rotational spectrum of CH₃CNO was measured in the frequency range 75 to 230 GHz. For the ground state, transitions were measured for J between 9 and 28 and for K from 0 to 12. In the v₁₀ = 1 state the measurements range from J = 0 to 19 and from K = 0 to 11. Numerous perturbations are observed, apparently due to accidental resonances with levels in other vibrational states. The contributions due to ΔK = 2, Δl = 2 matrix elements (l-type resonance and l-type doubling) are accounted for by matrix diagonalization, and the effects due to accidental resonances are presented graphically.     

Breakdown of an intermediate plateau in the magnetization process of anisotropic spin-1 Heisenberg dimer: Theory vs. experiment

The magnetization process of the spin-1 Heisenberg dimer model with the uniaxial or biaxial single-ion anisotropy is particularly investigated in connection with recent experimental high-field measurements performed on the single-crystal sample of the homodinuclear nickel(II) compound [Ni₂(Medpt)₂(μ-ox)(H₂O)₂](ClO₄)₂·2H₂O (Medpt=methyl-bis(3-aminopropyl)amine). The results obtained from the exact numerical diagonalization indicate a striking magnetization process with a marked spatial dependence on the applied magnetic field for arbitrary but finite single-ion anisotropy. It is demonstrated that the field range, which corresponds to an intermediate magnetization plateau emerging at a half of the saturation magnetization, basically depends on a single-ion anisotropy strength as well as a spatial orientation of the applied field. The breakdown of the intermediate magnetization plateau is discussed at length in relation to the single-ion anisotropy strength.     

Pressure broadening of the NH3 pure rotation line (JI = 0 → JF = 1) perturbed by inert gases (He,Ne, Ar,Kr)

We have calculated the linewidths of the NH₃ pure rotation line (J_I = 0 → J_F = 1) perturbed by inert gases (He, Ne, Ar, Kr) using a convergent impact theory. We have taken into account the dipole-induced dipole, quadrupole-induced dipole and dispersion terms of Krishnaji and Prakash and the dispersion term of Tipping and Herman. Our theoretical results and those obtained with the Anderson and Tsao and Curnette theory are compared with experimental results.     

Emergent nesting of the Fermi surface from local-moment description of iron-pnictide high-T<Subscript>c</Subscript> superconductors

We uncover the low-energy spectrum of a t-J model for electrons on a square lattice of spin-1 iron atoms with 3d _xz and 3d _yz orbital character by applying Schwinger-boson-slave-fermion mean-field theory and by exact diagonalization of one hole roaming over a 4 × 4 × 2 lattice. Hopping matrix elements are set to produce hole bands centered at zero two-dimensional (2D) momentum in the free-electron limit. Holes can propagate coherently in the t-J model below a threshold Hund coupling when long-range antiferromagnetic order across the d + = 3d _{(x + iy)z} and d ? = 3d _{(x ? iy)z} orbitals is established by magnetic frustration that is off-diagonal in the orbital indices. This leads to two hole-pocket Fermi surfaces centered at zero 2D momentum. Proximity to a commensurate spin-density wave (cSDW) that exists above the threshold Hund coupling results in emergent Fermi surface pockets about cSDW momenta at a quantum critical point (QCP). This motivates the introduction of a new Gutzwiller wavefunction for a cSDW metal state. Study of the spin-fluctuation spectrum at cSDW momenta indicates that the dispersion of the nested band of one-particle states that emerges is electron-type. Increasing Hund coupling past the QCP can push the hole-pocket Fermi surfaces centered at zero 2D momentum below the Fermi energy level, in agreement with recent determinations of the electronic structure of mono-layer iron-selenide superconductors.     

Influence of spin fluctuations in the ground state on the coherent motion of holes in high-T c superconductors

The coherent two-dimensional motion of a hole generated in a high-T _c superconductor at half-filling is discussed. The system is described by thet-J model which reduces to the Heisenberg antiferromagnet (HAF) at half-filling. Special attention is payed to the influence of spin fluctuations in the ground state on the hole motion. Spin fluctuations can be considered as deviations of the true ground state of the Heisenberg antiferromagnet from the Néel state. The calculations are based on the introduction of a new trial wave function. It generalizes a wave function which was originally proposed by Shraiman and Siggia for the hole motion in the Néel state. As a result, we find that the excitation energy for the hole has a bandwidth which is reduced by a factor 0.7 as compared to the case without spin fluctuations. Moreover, the dispersion relation contains cubic harmonics which are due to effective hopping processes to more distant than second-or third-nearest neighbors. For larger values of the ratiot/J the band is substantially deformed. We compare our theory with results obtained from the exact diagonalization of finite clusters and find good agreement.     

Theory of a single Oxygen hole propagating in Sr2CuO2Cl2: the spin of the quasiparticles in CuO2 planes

Recent photoemission experiments have measured E vs. k for a single hole propagating in antiferromagnetically aligned Sr₂CuO₂Cl₂. Comparisons with (i) the t - t′ - J model, for which the carrier is a spinless vacancy, and (ii) a strong-coupling version of the three-band Emery model, for which the carrier is a S = 1/2 hole moving on the Oxygen sublattice, have demonstrated that if one wishes to describe the quasiparticle throughout the entire first Brillouin zone the three-band model is superior. Here we present a new variational wave function for a single Oxygen hole in the three-band model: it utilizes a classical representation of the antiferromagnetically ordered Cuspin background but explicitly includes the quantum fluctuations of the lowest energy doublet of the Cu-O-Cu bond containing the Oxygen hole. We find that this wave function leads to a quasiparticle dispersion for physical exchange and hopping parameters that is in excellent agreement with the measured ARPES data. We also obtain the average spin of the Oxygen hole, and thus deduce that this spin is only quenched to zero at certain wave vectors, helping to explain the inadequacy of the t - t′ - J model to match the experimentally observed dispersion relation everywhere in the first Brillouin zone.     

Global Entanglement Measures and Quantum Phase Transitions in the 1D J 1? J 2 Model

We have analyzed the behavior of multipartite global entanglement and average bipartite concurrence for the sign of quantum phase transitions in the frustrated J ₁−J ₂ model by using exact diagonalization technique for a chain of 12 qubits. It is found that although the magnitude of two classes of the measures show opposite trends the absolute value of their derivatives show similar structure near critical points.     

Exact results for the diluted Ising model with competing interactions

We consider the random-bond Ising model with the exchange integrals J > 0, ?J and 0 with the respective probabilities p, q and r, where p + q + r = 1. We give the exact value of the averaged internal energy and an exact upper bound to the averaged specific heat at temperature T determined by $\text{k}{}_{\mathrm{B}}\text{T =}\text{2J}\text{In[}\text{p}\text{(1 ? p ? r)}\text{]}\text{,}$ where k_B is the Boltsmann constant. We show that all the averaged correlation functions of even spins are non-negative at this temperature.     

A precise solution of the rotation bending Schrödinger equation for a triatomic molecule with application to the water molecule

In this paper we report the results of improving the non-rigid bender formulation of the rotation-vibration Hamiltonian of a triatomic molecule [see A. R. Hoy and P. R. Bunker, J. Mol. Spectrosc., 52, 439 (1974)]. This improved Hamiltonian can be diagonalized as before by a combination of numerical integration and matrix diagonalization and it yields rotation-bending energies to high values of the rotational quantum numbers. We have calculated all the rotational energy levels up to J = 10 for the (v₁, v₂, v₃) states (0, 0, 0) and (0, 1, 0) for both H₂O and D₂O. By least squares fitting to the observations varying seven parameters we have refined the equilibrium structure and force field of the water molecule and have obtained a fit to the 375 experimental energies used with a root mean square deviation of 0.05 cm^?1. The equilibrium bond angle and bond length are determined to be 104.48° and 0.9578 Å respectively. We have also calculated these energy levels using the ab initio equilibrium geometry and force constants of Rosenberg, Ermler and Shavitt [J. Chem. Phys., 65, 4072 (1976)] and this is then the first complete ab initio calculation of rotation-vibration energy levels of high J in a polyatomic molecule to this precision. the rms fit of these ab initio energies to the experimental energies for the H₂O molecule is 2.65 cm^?1.     

Determination of the antiferromagnetic exchange constants between nearest-neighbour Mn2+ ions in Cd1-xMnxS and Zn1-xMnxSe

Steplike magnetization vs magnetic field dependence obtained in pulsed magnetic field up to 34 T in 1.8 K enables us to determine the value of the antiferromagnetic exchange constant between nearest-neighbour Mn²⁺ ion (J₁). The analysis of the first and the second step position in the framework of a generalized cluster model [1] yields J₁ = −8.6±0.9 K for Cd_0.945Mn_0.055 S and J₁ = −9.9±0.9 K for Zn_0.95 Mn_0.05 Se.     

The temperature-dependent phase diagrams of the spin-3/2 Ising model on a FM/AFM two-layer lattice with a crystal field

The temperature-dependent phase diagrams of the spin-3/2 Ising model on a two-layer Bethe lattice with ferromagnetic (FM)/antiferromagnetic (AFM) intra-layer and either FM or AFM type inter-layer interactions are investigated under a constant magnetic field (H) and in the presence of a crystal field (D) by using exact recursion equations in a pairwise approach for coordination numbers q=3,4 and 6, in detail. In the light of the ground-state (GS) phase diagrams, the temperature-dependent phase diagrams of the model are obtained by studying the thermal variations of the order parameters, response functions and free energy. Then, they are illustrated on the (kT/J₁,J₃/J₁) and (kT/J₁,J₂/J₁) planes for the given system parameters. It is observed that the system exhibits first- and second-order phase transitions for all q values, and hence, in some cases, tricritical points. The existence of critical-end points and that of isolated points are also observed. The re-entrant behavior owes its presence to the two Néel temperatures, T_N, that are present for all q.     

Macroscopic quantum tunneling in small magnetic particles

Macroscopic quantum tunneling of magnetization in small antiferromagnetic clusters is studied for the spin-1/2 anisotropic (J _z ≡ J, J _x =J _y ≡J _xy ) Heisenberg model with the use of both perturbation theory and an exact numerical diagonalization technique. Splitting of the two lowest levels due to the lifting of the degeneracy between them (in the case J _xy =0) by the in-plane exchange (J _xy ≠ 0) is found to occur in the N/2th order of perturbation theory. Tunneling is absent in systems with an odd number of sites, in which the levels are doubly degenerate in zero magnetic field. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 688–693 (10 May 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.