Exact ground state of the generalized three-dimensional Shastry-Sutherland model

We generalize the Shastry-Sutherland model to three dimensions. By representing the model as a sum of the semidefinite positive projection operators, we exactly prove that the model has exact dimer ground state. Several schemes for constructing the three-dimensional Shastry-Sutherland model are proposed. Received 20 February 2002 / Received in final form 27 May 2002 Published online 17 September 2002     

Exact solution of new integrable nineteen-vertex models and quantum spin-1 chains

New exactly solvable nineteen vertex models and related quantum spin-1 chains are solved. Partition functions, excitation energies, correlation lengths, and critical exponents are calculated. It is argued that one of the non-critical Hamiltonians is a realization of an integrable Haldane system. The finite-size spectra of the critical Hamiltonians deviate in their structure from standard predictions by conformal invariance.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Scaling behaviour of the energy gap of spin-1/2 AF-Heisenberg chains in both uniform and staggered fields

The energy gap of the 1D AF-Heisenberg model in the presence of both uniform (H) and staggered (h) magnetic fields is investigated using the exact diagonalization technique. The opening of the gap in the presence of a staggered field is found to scale with h^ν, where ν=ν(H) is the critical exponent, and depends on the uniform field. With respect to the range of the staggered magnetic field, two regimes are identified through which the dependence of the real critical exponent ν(H) on H can be calculated numerically. Our numerical results are in good agreement with the results obtained by other theoretical approaches.     

Quantum spin-{3 \over 2} models on the Cayley tree - optimum ground state approach

We present a class of optimum ground states for quantum spin- models on the Cayley tree with coordination number 3. The interaction is restricted to nearest neighbours and contains 5 continuous parameters. For all values of these parameters the Hamiltonian has parity invariance, spin-flip invariance, and rotational symmetry in the xy-plane of spin space. The global ground states are constructed in terms of a 1-parametric vertex state model, which is a direct generalization of the well-known matrix product ground state approach. By using recursion relations and the transfer matrix technique we derive exact analytical expressions for local fluctuations and longitudinal and transversal two-point correlation functions. Received 1 March 1999     

Exactly solvable spin ladder model with degenerate ferromagnetic and singlet states

We study the spin ladder model with interactions between spins on neighboring rungs. The model Hamiltonian with the exact singlet ground state degenerated with ferromagnetic state is obtained. The singlet ground state wave function has a special recurrent form and depends on two parameters. Spin correlations in the singlet ground state show double-spiral structure with period of spirals equals to the system size. For special values of parameters they have exponential decay. The spectrum of the model is gapless and there are asymptotically degenerated excited states for special values of parameters in the thermodynamic limit. Received 7 May 1999     

Far-infrared probe of size dispersion and population fluctuations in doped self-assembled quantum dots

We investigate the FIR magneto-optical transitions in doped self-assembled InAs quantum dots with an average filling ranging from 0.6 to 6 electrons per dot. Significant changes in the magnetic field dispersion, the line-width and the amplitude of the transitions are observed as the doping level is varied, in agreement with our theoretical calculations. We show that our technique is an effective tool to obtain informations regarding the dot size homogeneity and the electron filling uniformity.Received: 22 July 2003, Published online: 2 October 2003PACS: 73.21.La Quantum dots - 78.20.Ls Magnetooptical effects - 78.30.Fs III-V and II-VI semiconductors - 78.67.Hc Quantum dotsE. Deleporte: Present address: Laboratoire de Photonique Quantique et Moleculaire, École Normale Superieure de Cachan, 94235 Cachan Cedex, FranceJ.M. Gérard: Present address: CEA-Grenoble DRFMC/SP2M/PSC, Laboratoire de Physique des semiconducteurs, 38054 Grenoble, France     

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     

Phase diagram of frustrated mixed-spin ladders in the strong-coupling limit

We study the ground-state properties of frustrated Heisenberg ferrimagnetic ladders with antiferromagnetic exchange interactions and two types of alternating sublattice spins. In the limit of strong rung couplings, we show that the mixed spin-1/2 and spin-1 ladders can be systematically mapped onto a spin-1/2 Heisenberg model with additional next-nearest-neighbor exchanges. The system is either in a ferrimagnetic state or in a critical spin-liquid state depending on the competition between the spin exchanges along the legs and the diagonal exchanges.     

Thermodynamics of the anisotropic spin-1/2 Heisenberg chain and related quantum chains

The free energy and correlation lengths of the spin-1/2XYZ chain are studied at finite temperature. We use the quantum transfer matrix approach and derive non-linear integral equations for all eigenvalues. Analytic results are presented for the low-temperature asymptotics, in particular for the criticalXXZ chain in an external magnetic field. These results are compared to predictions by conformal field theory. The integral equations are solved numerically for the non-criticalXXZ chain and the related spin-1 biquadratic chain at arbitrary temperature.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Novel massive ground states of spin chains in a magnetic field

Novel massive quantum states appearing in spin chains under a strong magnetic field are discussed. These states lead to plateaus in magnetization curves. When the systems are axially symmetric and the field is applied parallel to the symmetry-axis, the phenomena are analogous to metal-insulator transitions. Striking features of the plateau phenomena - exactness and rationality - are explained as consequences the commensurability condition to the underlying lattice. The effects of the planar anisotropy are also discussed in detail. Received: 16 February 1998 / Revised: 20 April 1998 / Accepted: 30 April 1998     

Long-range spin-pairing order and spin defects in quantum spin- $${1 \over 2}$$ ladders

For w-legged antiferromagnetic spin-1/2 Heisenberg ladders, a long-range spin pairing order can be identified which enables the separation of the space spanned by finite-range (covalent) valence-bond configurations into w +1 subspaces. Since every subspace has an equivalent counter subspace connected by translational symmetry, twofold degeneracy, breaking translational symmetry is found except for the subspace where the ground state of w = even belongs to. In terms of energy ordering, (non)degeneracy and the discontinuities introduced in the long-range spin pairing order by topological spin defects, the differences between even and odd ladders are explained in a general and systematic way. Received 19 July 1999 and Received in final form 8 October 1999     

Exact ground state of a spin ladder with a quantum phase transition

We introduce a spin ladder with Ising interactions along the legs and intrinsically frustrated Heisenberg-like ferromagnetic interactions on the rungs. The model is solved exactly in the subspaces relevant for the ground state by mapping to the quantum Ising model, and we show that a first order quantum phase transition separates the classical from quantum regime, with the spin correlations on the rungs being either ferromagnetic or antiferromagnetic, and different spin excitations in both regimes. The present case resembles the quantum phase transition found in the compass model in one and two dimensions.     

Quantum corrections of the Dzyaloshinskii-Moriya interaction on the spin-$\frac{1}{2}$ AF-Heisenberg chain in an uniform magnetic field

We have investigated the ground state phase diagram of the 1D AF spin- Heisenberg model with the staggered Dzyaloshinskii-Moriya (DM) interaction in an external uniform magnetic field H. We have used the exact diagonalization technique. In the absence of the uniform magnetic field (H=0), we have shown that the DM interaction induces a staggered chiral phase. The staggered chiral phase remains stable even in the presence of the uniform magnetic field. We have identified that the ground state phase diagram consists of four Luttinger liquid, staggered chiral, spin-flop, and ferromagnetic phases.     

Magnetic excitations in charge ordered a' - {N_a}{V_2}{O_5}

An investigation of the spin excitation spectrum of charge ordered (CO) NaV₂O₅ is presented. We discuss several different exchange models which may be relevant for this compound, namely in-line and zig-zag chain models with weak as well as strong inter-chain coupling and also a ladder model and a CO/MV (mixed valent) model. We put special emphasis on the importance of large additional exchange across the diagonals of V-ladders and the presence of exchange anisotropies on the excitation spectrum. It is shown that the observed splitting of transverse dispersion branches may both be interpreted as anisotropy effect as well as acoustic-optic mode splitting in the weakly coupled chain models. In addition we calculate the field dependence of excitation modes in these models. Furthermore we show that for strong inter-chain coupling, as suggested by recent LDA + U results, an additional high energy optical excitation appears and the spin gap is determined by anisotropies. The most promising CO/MV model predicts a spin wave dispersion perpendicular to the chains which agrees very well with recent results obtained by inelastic neutron scattering. Received 30 April 1999 and Received in final form 5 October 1999     

Electron-phonon interaction in carbon clathrate hex- $\mathsf{C_{40}}$

We investigate an extended spin ladder with diagonal frustrated exchanges in a wide parameter regime. By representing the model as a sum of semidefinite positive projection operators, we prove that this model has exactly a dimer ground state. Smoothly changing parameters may lead the model cover several exactly known models. Starting from this ladder model, we proposed two two-dimensional net models with exact ground states. The quantum phase transition of the ground state, due to the change of exchange strengths along perpendicular rungs, is also discussed. Received 13 October 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: schen@thphy.uni.duesseldorf.de     

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     

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.     

Low temperature thermodynamics of inverse square spin models in one dimension

We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility at low temperatures is shown to diverge like with a=(N-2)/(N-1) and . From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also to ferromagnetic quantum spin chains. Received: 20 February 1998 / Revised: 27 April 1998 / Accepted: 30 April 1998     

Quantum rotors with regular frustration and the quantum Lifshitz point

We have discussed the zero-temperature quantum phase transition in n-component quantum rotor Hamiltonian in the presence of regular frustration in the interaction. The phase diagram consists of ferromagnetic, helical and quantum paramagnetic phase, where the ferro-para and the helical-para phase boundary meets at a multicritical point called a (d,m) quantum Lifshitz point where (d,m) indicates that the m of the d spatial dimensions incorporate frustration. We have studied the Hamiltonian in the vicinity of the quantum Lifshitz point in the spherical limit and also studied the renormalisation group flow behaviour using standard momentum space renormalisation technique (for finite n). In the spherical limit ()one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m =d though the quantum Lifshitz point exists for all d > 1+m/2, and the upper critical dimensionality is given by d _u = 3 +m/2. The scaling behaviour in the neighbourhood of a quantum Lifshitz point in d dimensions is consistent with the behaviour near the classical Lifshitz point in (d+z) dimensions. The dynamical exponent of the quantum Hamiltonian z is unity in the case of anisotropic Lifshitz point (d>m) whereas z=2 in the case of isotropic Lifshitz point (d=m). We have evaluated all the exponents using the renormalisation flow equations along-with the scaling relations near the quantum Lifshitz point. We have also obtained the exponents in the spherical limit (). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian model by Fisher renormalisation. Received: 23 December 1997 / Received in final form: 6 January 1998 / Accepted: 7 January 1998     

On evaluation of transverse spin fluctuations in quantum magnets

A numerical method is described for evaluating transverse spin correlations in the random phase approximation. Quantum spin-fluctuation corrections to sublattice magnetization are evaluated for the antiferromagnetic ground state of the half-filled Hubbard model in two and three dimensions in the whole U/t range. Extension to the case of defects in the AF is also discussed for spin vacancies and low-U impurities. In the limit, the vacancy-induced enhancement in the spin fluctuation correction is obtained for the spin-vacancy problem in two dimensions, for vacancy concentration up to the percolation threshold. For low-U impurities, the overall spin fluctuation correction is found to be strongly suppressed, although surprisingly spin fluctuations are locally enhanced at the low-U sites. Received 27 April 1998 and Received in final form 13 August 1998