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We have performed a numerical investigation of the ground state properties of the frustrated quantum Heisenberg antiferromagnet on the square lattice ("J 1 − J 2 model"), using exact diagonalization of finite clusters with 16, 20, 32, and 36 sites. Using a finite-size scaling analysis we obtain results for a number of physical properties: magnetic order parameters, ground state energy, and magnetic susceptibility (at q = 0). For the unfrustrated case these results agree with series expansions and quantum Monte Carlo calculations to within a percent or better. In order to assess the reliability of our calculations, we also investigate regions of parameter space with well-established magnetic order, in particular the non-frustrated case J 2 < 0. We find that in many cases, in particular for the intermediate region 0.3 < J 2 /J 1 < 0.7, the 16 site cluster shows anomalous finite size effects. Omitting this cluster from the analysis, our principal result is that there is Néel type order for J 2 /J 1 < 0.34 and collinear magnetic order (wavevector Q = (0, π)) for J 2 /J 1 > 0.68. There thus is a region in parameter space without any form of magnetic order. Including the 16 site cluster, or analyzing the independently calculated magnetic susceptibility we arrive at the same conclusion, but with modified values for the range of existence of the nonmagnetic region. We also find numerical values for the spin-wave velocity and the spin stiffness. The spin-wave velocity remains finite at the magnetic-nonmagnetic transition, as expected from the nonlinear sigma model analogy. 75.10.Jm, 75.40.Mg

Using results for the 4 x 4 and 6 x 6 lattice, we produce the first finite-size scaling analysis of the frustrated Heisenberg model in two dimensions. The results indicate a continuous phase transition from the ordered phase into an intermediate phase without long-range magnetic order, as for the (2 + 1)-dimensional nonlinear sigma-model. The intermediate phase is stable for 0.4 < J 2 / J I < 0.65 and exhibits either dimerization or broken chiral symmetry. The transition to the collinear phase at J z / J 1 = 0.65 is apparently of first order.

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The Dzyaloshinski-Moriya interaction partially lifts the magnetic frustration of the spin-1/2 oxide SrCu2(BO3)2. It explains the fine structure of the excited triplet state and its unusual magnetic field dependence, as observed in previous ESR and new neutron inelastic scattering experiments. We claim that it is mainly responsible for the dispersion. We propose also a new mechanism for the observed ESR transitions forbidden by standard selection rules, that relies on an instantaneous Dzyaloshinski-Moriya interaction induced by spin-phonon couplings. PACS numbers:Strontium Copper Borate (SrCu 2 (BO 3 ) 2 ) is a new example of a magnetic oxide with a spin gap [1], with a ground state well described as simply a product of magnetic dimers in two dimensions on the bonds giving the strongest magnetic exchange [2]. The weaker exchanges are frustrated by the geometry and, as shown by Shastry and Sutherland [3], the ground state of the isotropic Hamiltonian is independent of the value of the weaker exchange, up to a critical value. The excitations, however, are not purely local and cannot be explicitly given. Recent experiments by ESR [4] and neutron inelastic scattering presented here show how in fact there are spin anisotropies needed for an accurate description of the dynamics. We shall show the corrections to the ground state are needed that, while small, will be necessary to understand many physical properties. For example at finite external magnetic field SrCu 2 (BO 3 ) 2 appears to exhibit a number of finite magnetization plateaux [1,5], and the anisotropies will determine the observability of plateaux in different field directions. Furthermore SrCu 2 (BO 3 ) 2 is believed to be close in parameter space to a quantum critical point whose nature is somewhat controversial, and while the anisotropies are small they may be essential to its nature.For spin 1 2 the leading anisotropic terms are of form Dzyaloshinski-Moriya [6] and exchange anisotropy. The former is particularly relevant, since it may not be frustrated even if the isotropic exchange is. While a small Dzyaloshinski-Moriya interaction should not destroy a gap generated by larger isotropic interactions it modifies the pure locality of the ground state correlations and delocalizes the first triplet excitation. This is because it appears in lower order in perturbation theory than the frustrated isotropic interactions. In this paper we predict the Dzyaloshinski-Moriya interactions that should be expected in SrCu 2 (BO 3 ) 2 from the structure, and show that they do indeed explain new features of the excitations observed with ESR and neutron inelastic scattering experiments. Miyahara and Ueda [2] have introduced the frustrated Shastry-Sutherland modelfor SrCu 2 (BO 3 ) 2 , with S = 1/2 and where nn stands for nearest neighbor spins and nnn for next nearest neighbors. The lattice is shown in fig. 1. J = 85K and J ′ = 54K are antiferromagnetic interactions estimated from the susceptibility and the gap [2]. The spectrum of spin excitations has several interesting f...

We calculate the level statistics by finding the eigenvalue spectrum for a variety of one-dimensional many-body models, namely the Heisenberg chain, the t-J model and the Hubbard model. In each case the generic behaviour is GOE, however at points corresponding to models known to be exactly integrable Poisson statistics are found, in agreement with an argument we outline.

We present a semi-analytic theory for the Curie temperature in diluted magnetic semi-conductors that treats disorder effects exactly in the effective Heisenberg Hamiltonian, and spin fluctuations within a local RPA. The exchange couplings are taken from concentration dependentab initio estimates. The theory gives very good agreement with published data for wellannealed samples of Mn x Ga 1−x As. We predict the critical temperatures for Mn x Ga 1−x N lower than in doped GaAs, despite the stronger nearestneighbour ferromagnetic coupling. We also predict the dependence on the hole concentration.Search for diluted magnetic semiconductors with ferromagnetism stable to high temperatures has been hampered by the many physical parameters that may determine magnetic properties. These include the choice of host semiconductor, that of the doping magnetic impurity, the degree of compensation, and methods of preparation and treatment of the sample [1]. The underlying mechanism of interaction between dopant spins has without doubt been correctly identified: Ruderman-Kittel-Kasuya-Yosida(RKKY)-like effective interactions mediated by both the host [2,3] and the doping band [4-6]. Despite this, the theory has not lead to reliable quantitative predictions. Comparison of calculations has been complicated by difficulties of full characterizing the samples. In samples of GaAs doped with Mn, extensive experimental studies [1] have now allowed for greater control over sample parameters and there is now apparently convergence to reliable experimental values of the critical temperature of different groups [7-10]. An important factor was that the carrier densities were measured simultaneously by magneto-transport. There is now the possibility of testing calculations against experiments and determining the origin of past discrepancies.Ab initio calculations using the Local Density Approximation and the magnetic force theorem can be used [5] to derive realistic values of magnetic exchange interactions between classical impurity spins. These calculations also take into account the effect on the effective exchange of disorder of the carriers, within a Coherent Potential Approximation (CPA). Similar calculations based on supercells [12,13] lead to comparable results at low concentration. It has become apparent that the difficulty is not in deriving the effective magnetic Hamiltonian correctly but in treating its thermodynamics accurately. As we will demonstrate explicitly here, treating the magnetic correlations by over-simplified mean field theories [14,15] has lead to overstatement , by a wide margin, of the critical temperature T c . The disorder in the effective magnetic model also plays an important role that cannot be simply treated by an effective medium theory of the style of the Virtual Crystal Approximation (VCA) [16]. This suggests that the discrepancy with experiment is largely due to approximations made to the effective Hamiltonian, not the values of the couplings themselves. Thus by improving the treatment of the effective Hamilt...