First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

Ground-state long-range order in quasi-one-dimensional Heisenberg quantum antiferromagnets: high-order coupled-cluster calculations

We investigate the ground-state magnetic long-range order of quasi-one-dimensional quantum Heisenberg antiferromagnets for spin quantum numbers s = 1/2 and s = 1. We use the coupled cluster method to calculate the sublattice magnetization and its dependence on the inter-chain coupling J_⊥. We find that for the unfrustrated spin-1/2 system, an infinitesimal inter-chain coupling is sufficient to stabilize magnetic long-range order, in agreement with results obtained by other methods. For s = 1, we find that a finite inter-chain coupling is necessary to stabilize magnetic long-range order. Furthermore, we consider a quasi one-dimensional spin-1/2 system, where a frustrating next-nearest neighbor in-chain coupling is included. We find that for stronger frustration as well, a finite inter-chain coupling is necessary to have magnetic long-range order in the ground state, and that the strength of the inter-chain coupling necessary to establish magnetic long-range order is related to the size of the spin gap of the isolated chain.     

Macroscopic quantum coherence of the Neel vector in antiferromagnetic system without Kramers' degeneracy

At low temperatures the Neel vector in a small antiferromagnetic particle can possess quantum coherence between the classically degenerate minima. In some cases, the topological term in the magnetic action can lead to destructive interference between the symmetry-related trajectories for the half-integer excess spin antiferromagnetic particle. By studying a macroscopic quantum coherence problem of the Neel vector with biaxial crystal symmetry and a weak magnetic field applied along the hard axis, we find that the quenching of tunnel splitting could take place in the system without Kramers' degeneracy. Both the Wentzel-Kramers-Brillouin exponent and the pre-exponential factors are found exactly for the tunnel splitting. Results show that the tunnel splitting oscillates with the weak applied magnetic field for both the integer and half-integer excess spin antiferromagnetic particles, and vanishes at certain values of the field. All the calculations are performed based on the two sublattices model and the instanton method in spin-coherent-state path integral. Received: 24 July 1997 / Accepted: 30 September 1997     

The spin-1/2 anisotropic Heisenberg-chain in longitudinal aaand transversal magnetic fields: a DMRG study

Using the density matrix renormalization group technique, we evaluate the low-energy spectrum (ground state and first excited states) of the anisotropic antiferromagnetic spin-one-half chain under magnetic fields. We study both homogeneous longitudinal and transversal fields as well as the influence of a transversal staggered field on the opening of a spin-gap. We find that only a staggered transversal field opens a substantial gap. Received 16 April 2002 / Received in final form 4 July 2002 Published online 17 September 2002     

Optical properties of multilayer structures

This paper describes the magneto-optical effects of metallic multilayers under the condition of total internal reflection. In the framework of the Green's dyadic technique, we present numerical simulations which account for the variation of the magneto-optical signal with the angle of incidence. The Attenuated Total Reflection (ATR) has become a new technique of characterization for thin films. We show, in this paper, optical effects due to a slight variation of the indice of refraction for thin dielectric films in reflection by the reflectivity and the Kerr rotation spectra of an optimized system. In transmission, this variation is brought to the fore by the near-field intensity spectra. Received 29 March 2000     

Solitons in the spin-Peierls compound CuGeO <Subscript>3</Subscript>

We calculate the excitation gap, the soliton energy, and the soliton density at finite temperature, of the spin-1/2 one dimensional antiferromagnet coupled to phonons, using a self-consistent harmonic approximation, and the thermal-Green function technique. The spin degrees of freedom are represented by the phase Hamiltonian with the help of the boson representation of the spinless fermions. We estimate the critical field H_c above which begins the incommensurate phase. We also present a theoretical calculation for the specific heat in this phase. We use CuGeO₃ as an example of a compound where our theory could be applied. Received 22 October 2002 / Received in final form 21 January 2003 Published online 14 March 2003     

On the origin of biquadratic exchange in spin 1 chains

One-dimensional spin 1 systems may have a rich phase diagram including Haldane gap and dimerized phases if the usually very small biquadratic exchange becomes significant. We show that this unlikely condition may be fulfilled in electron systems with quasi-degenerate orbitals. This mechanism may have been experimentally realized in the spin 1 chain LiVGe₂O₆. The implications for the exploration of the physics and quantum chemistry of spin 1 chains are discussed. Received 4 January 2000     

A spin- {1 \over 2} model for CsCuCl3 in an external magnetic field

CsCuCl₃ is a ferromagnetically stacked triangular spin-1/2 antiferromagnet. We discuss models for its zero-temperature magnetization process. The models range from three antiferromagnetically coupled ferromagnetic chains to the full three-dimensional situation. The situation with spin-1/2 is treated by expansions around the Ising limit and exact diagonalization. Further, weak-coupling perturbation theory is used mainly for three coupled chains which are also investigated numerically using the density-matrix renormalization group technique. We find that already the three-chain model gives rise to the plateau-like feature at one third of the saturation magnetization which is observed in magnetization experiments on CsCuCl₃ for a magnetic field perpendicular to the crystal axis. For a magnetic field parallel to the crystal axis, a jump is observed in the experimental magnetization curve in the region of again about one third of the saturation magnetization. In contrast to earlier spinwave computations, we do not find any evidence for such a jump with the model in the appropriate parameter region. Received 25 October 1999 and Received in final form 30 December 1999     

Quasiclassical Hamiltonians for large-spin systems

We extend and apply a previously developed method for a semiclassical treatment of a system with large spin S. A multisite Heisenberg Hamiltonian is transformed into an effective classical Hamilton function which can be treated by standard methods for classical systems. Quantum effects enter in form of multispin interactions in the Hamilton function. The latter is written in the form of an expansion in powers of J/(TS), where J is the coupling constant. Main ingredients of our method are spin coherent states and cumulants. Rules and diagrams are derived for computing cumulants of groups of operators entering the Hamiltonian. The theory is illustrated by calculating the quantum corrections to the free energy of a Heisenberg chain which were previously computed by a Wigner-Kirkwood expansion. Received 5 May 1999 and received in final form 24 September 1999     

Uniform susceptibility of classical antiferromagnets in one and two dimensions in a magnetic field

We simulated the field-dependent magnetization m(H,T) and the uniform susceptibility of classical Heisenberg antiferromagnets in the chain and square-lattice geometry using Monte Carlo methods. The results confirm the singular behavior of at small T,H: and , where D=3 is the number of spin components, J ₀=zJ, and z is the number of nearest neighbors. A good agreement is achieved in a wide range of temperatures T and magnetic fields H with the first-order 1/D expansion results (D.A. Garanin, J. Stat. Phys. 83, 907 (1996)). Received 20 March 2000     

Magnetic field induced ordering in quasi-one-dimensional quantum magnets

Three-dimensional magnetic ordering transitions are studied theoretically in strongly anisotropic quantum magnets. An external magnetic field can drive quasi-one-dimensional subsystems with a spin gap into a gapless regime, thus inducing long-range three-dimensional magnetic ordering due to weak residual magnetic coupling between the subsystems. Compounds with higher spin degrees of freedom, such as N-leg spin-1/2 ladders, are shown to have cascades of ordering transitions. At high magnetic fields, zero-point fluctuations within the quasi-1D subsystems are suppressed, causing quantum corrections to the ordering temperature to be reduced. Received 24 March 2000     

Degeneracy of the ground-state of antiferromagnetic spin-1/2 Hamiltonians

In the first part of this paper, the extension of the Lieb-Schultz-Mattis theorem to dimensions larger than one is discussed. A counter example to the original formulation of Lieb-Schultz-Mattis and Affleck is exhibited and a more precise statement is formulated. The degeneracy of the ground-state in symmetry breaking phases with long-range order is analyzed. The second and third parts of the paper concern resonating valence-bond (RVB) spin liquids. In these phases the relationship between various authors approaches: Laughlin-Oshikawa, Sutherland, Rokhsar and Kivelson, Read and Chakraborty and the Lieb-Schultz-Mattis-Affleck proposal is studied. The deep physical relation between the degeneracy property and the absence of stiffness is explained and illustrated numerically. A new conjecture is formed concerning the absolute absence of sensitivity of the spin liquid ground-states to any twist of the boundary conditions (thermodynamic limit). In the third part of the paper the relations between the quantum numbers of the degenerate multiplets of the spin liquid phases are obtained exactly. Their relationship with a topological property of the wave functions of the low lying levels of this spin liquid phase is emphasized. In spite of the degeneracy of the ground-state, we explain why these phases cannot exhibit spontaneous symmetry breaking. Received 19 December 2001     

Series expansion analysis of a tetrahedral cluster spin chain

Using analytical series expansion by continuous unitary transformations we study the magnetic properties of a frustrated tetrahedral spin- chain. Starting from the limit of isolated tetrahedra we analyze the evolution of the ground state energy and the elementary triplet dispersion as a function of the inter-tetrahedral coupling. The quantum phase diagram is evaluated and is shown to incorporate a singlet product, a dimer, and a Haldane phase. Comparison of our results with those from several other techniques, such as density matrix renormalization group, exact diagonalization, bond-operator theory and other numerical series expansion are provided and convincing agreement is found.     

Ladders in a magnetic field: a strong coupling approach

We show that non-frustrated and frustrated ladders in a magnetic field can be systematically mapped onto an XXZ Heisenberg model in a longitudinal magnetic field in the limit where the rung coupling is the dominant one. This mapping is valid in the critical region where the magnetization goes from zero to saturation. It allows one to relate the properties of the critical phase (H _c ¹, H _c ², the critical exponents) to the exchange integrals and provide quantitative estimates of the frustration needed to create a plateau at half the saturation value for different models of frustration. Received: 7 May 1998 / Revised and Accepted: 10 July 1998     

Spin-liquid state for two-dimensional Heisenberg antiferromagnets on a kagomé lattice

The magnetic properties of the spin liquid state of the antiferromagnetic Heisenberg model on the kagomé lattice are investigated within the self-consistent mean-field theory. The results show that the spin liquid ground-state energy per site is , which is in very good agreement with the best numerical estimates. The spin structure factor and spin susceptibility are also discussed. Received 1 December 1998 and Received in final form 12 April 1999     

Modified spin-wave theory for the S = 1 frustrated antiferromagnetic Heisenberg chain

We study the one-dimensional isotropic spin-1 Heisenberg magnet with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions by using the modified spin wave theory (MSWT). The ground state energy and the singlet-triplet energy gap are obtained for several values of j, defined as the ratio of the nnn interaction constant to the nn one. We also compare two different ways of implementing the MSWT currently found in the literature, and show that, despite the remarkable differences between the equations to be solved in each procedure, the results given by both are equivalent, except for the predicted value of the j_max, the maximum value of j accessible in each treatment. Here, we suggest that j_max is related to the disorder point of the first kind. Our results show that the ground state and the gap energies increase with j, for j ≤j_max, in accordance to previous numerical results.     

A generalized spin ladder in a magnetic field

We study the phase diagram of coupled spin-1/2 chains with bilinear and (chiral) three-spin exchange interactions in a magnetic field. The model is soluble on a one-parametric line in the space of coupling constants connecting the limiting cases of a single and two decoupled Heisenberg chains with nearest neighbour exchange only. We give a complete classification of the low-energy properties of the integrable system and introduce a numerical method which allows to study the possible phases of spin ladder systems away from the soluble line in a magnetic field. Received 17 November 1998 and Received in final form 22 January 1999     

Vortices in quantum spin systems

We examine spin vortices in ferromagnetic quantum Heisenberg models with planar anisotropy on two-dimensional lattices. The symmetry properties and the time evolution of vortices built up from spin-coherent states are studied in detail. Although these states show a dispersion typical for wave packets, important features of classical vortices are conserved. Moreover, the results on symmetry properties provide a construction scheme for vortex-like excitations from exact eigenstates, which have a well-controlled time evolution. Our approach works for arbitrary spin length both on triangular and square lattices. Received 2 October 1998