We argue that the S =1/ 2 kagome antiferromagnet undergoes a quantum phase transition when the Dzyaloshinskii-Moriya coupling is increased. For D Ͻ D c the system is in a moment-free phase, and for D Ͼ D c the system develops antiferromagnetic long-range order. The quantum critical point is found to be D c Ӎ 0.1J using exact diagonalizations and finite-size scaling. This suggests that the kagome compound ZnCu 3 ͑OH͒ 6 Cl 3 may be in a quantum critical region controlled by this fixed point.

The ground-state wave function for the spin-2 quantum antiferromagnet on a 36-site kagome structure is found by numerical diagonalization. Spin-spin correlations and spin gaps indicate that the ground state of this system does not possess magnetic order. The spin-Peierls order is studied using a four-spin correlation function. The short-range structure in this correlation function is found to be consistent with a simple dimer-liquid model.

We present results of an exact diagonalization calculation of the spectral function A(k, ω) for a single hole described by the t-J model propagating on a 32-site square cluster. The minimum energy state is found at a crystal momentum k = ( π 2 , π 2 ), consistent with theory, and our measured dispersion relation agrees well with that determined using the self-consistent Born approximation. In contrast to smaller cluster studies, our spectra show no evidence of string resonances. We also make a qualitative comparison of the variation of the spectral weight in various regions of the first Brillouin zone with recent ARPES data. PACS: 71.27.+a, 74.25.Jb, 75.10.Jm Typeset using REVT E X 1The t-J model has received a lot of attention in recent years. It is believed to be the simplest strong-coupling model of the low energy physics of the anomalous metallic state of high-temperature superconductors [1,2]. The Hamiltonian of the model iswhere ij denotes nearest neighbor sites, andc † iσ ,c iσ are the constrained operators,c iσ = In this paper we report the first exact diagonalization results, found using the Lanczos algorithm, for a single hole described by the t-J model on a 32-site square lattice. We use t as the unit of energy, i.e., t = 1. Figure 1 shows the distinct k points in the reciprocal space of the 32-site square lattice. Previous calculations for this model were mostly done on the 16-site (4 × 4) square lattice, where the k points along the antiferromagnetic Brillouin zone (ABZ) edge (from (0, π) to (π, 0)) are degenerate. Other square lattices that have been studied (18-, 20-, and 26-site) do not have the important k points along the ABZ edge, viz., the single-hole ground state wavevector () nor many points along the (1, 1) direction (from (0, 0) to (π, π)). The 32-site square lattice is the smallest one which has these high symmetry points, and does not have the spurious degeneracy of the 4 × 4 square lattice.2 Thus, this paper represents a major advance in the exact, unbiased, numerical treatment of an important strong-coupling Hamiltonian.In order for us to complete the exact diagonalization on such a large lattice, we use translation and one reflection symmetry to reduce the total number of basis states to about), no reflection symmetry can be used and the total number of basis states is about 300 million. To study the effect of finite system sizes, we will supplement our results with data obtained from smaller systems: the N = 16 (4 × 4) cluster, as well as a 24-site ( √ 18 × √ 32) cluster that includes many of the important wave vectors [7].The electron spectral function is defined bywhere E [8] with 300 iterations and an artificial broadening factor ǫ = 0.05. We obtain A(k, ω) that are well converged using these quantities.Figure 2(a) shows A(k, ω) at J = 0.3 from (0, 0) to (π, π). At (0, 0), the spectrum has a quasiparticle peak at ω ∼ 1.34 and a broad feature at lower energies. As k moves away from (0, 0) along the (1, 1) direction towards (π, π), spectral weight shifts from the broad ...

The spin-2 anisotropic Heisenberg antiferromagnet is studied at T = 0 on the triangular lattice via numerical diagonalization for system sizes up to N = 36 sites. Extrapolation to the thermodynamic limit suggests that the isotropic system possesses no, or very small,~3 x~3 magnetic order; no helical or chiral order; and spin-spin correlations consistent with that of a critical phase. For A Y-like anisotropy there is long-ranged~3x~3 magnetic order. In contrast to bipartite lattices, the standard firstand second-order spin-wave theories are not quantitatively accurate. Excitation energy gaps suggest that the lowest-lying excitations for the isotropic point are not spin-Rip excitations in the thermodynamic limit. The results for the isotropic point appear to agree with recent series expansion, large-N expansion, and the original resonanting valence bond picture of Anderson, although they cannot be considered as conclusive evidence supporting any of these theories.

We study the nature of the ground state of the quantum dimer model proposed by Rokhsar and Kivelson by diagonalizing the Hamiltonian of the model on square lattices of size LϫL, where Lр8, with periodic boundary conditions. Finite-size scaling studies of the columnar order parameter and the low lying excitation spectrum show no evidence of a dimer liquid state in any finite region of the zero temperature phase diagram. In addition, we find evidence of a transition from the columnar dimer state to an intermediate state at a negative value of V/J. This state is consistent with the plaquette resonating-valence-bond state. The energy gap of this state vanishes as a power law of L. It exhibits columnar dimer order, but has disorder within the dimer columns. This state persists up to V/JϽ1, and the system changes to a dimer liquid state only at V/Jϭ1.

The magnetic phase diagrams, and other physical characteristics, of the hole-doped La2 Sr Cu04 and electron-doped Ndq Ce Cu04 high-temperature superconductors are profoundly different. Given that it is envisaged that the simplest Hamiltonians describing these systems are the same, viz. , the t-t'-J model, this is surprising. Here we relate these physical differences to their ground states single-hole quasiparticles, the spin distortions they produce, and the spatial distribution of carriers for the multiply doped systems. As is well known, the low doping limit of the hole-doped material corresponds to k = ( -, -) quasiparticles, states that generate so-called Shraiman-Siggia long-ranged dipolar spin distortions via back6ow. These quasiparticles have been proposed to lead to an incommensurate spiral phase, an unusual scaling of the magnetic susceptibility, as well as the scaling of the correlation length defined by ( (z, T) = ( (z, O) + ( (O, T), all consistent with experiment. We suggest that for the electron-doped materials the single-hole ground state corresponds to k = (s, O) quasiparticles; we show that the spin distortions generated by such carriers are shortranged. Then, we demonstrate the effect of this single-carrier difference in many-carrier ground states via exact diagonalization results by evaluating S(q) for up to four carriers in small clusters. Consistent with experiment, for the hole-doped materials short-ranged incommensurate spin orderings are induced, whereas for the electron-doped system only commensurate spin correlations are found. Further, we propose that there is an important difference between the spatial distributions of mobile carriers for these two systems: for the hole-doped material the quasiparticles tend to stay far apart from one another, whereas for the electron-doped material we find tendencies consistent with the clustering of carriers, and possibly of low-energy Buctuations into an electronic phase-separated state. Phase separation in this material is consistent with the midgap states found by recent angle-resolved photoemission spectroscopy studies. Last, we propose the extrapolation of an approach based on the t-t'-J model to the hole-doped 123 system.

The t-J z model is the strongly anisotropic limit of the t-J model which captures some general properties of doped antiferromagnets ͑AF's͒. The absence of spin fluctuations simplifies the analytical treatment of hole motion in an AF background, and allows us to calculate single-and two-hole spectra with a high accuracy using a regular diagram technique combined with a real-space approach. At the same time, numerical studies of this model via exact diagonalization on small clusters show negligible finite-size effects for a number of quantities, thus allowing a direct comparison between analytical and numerical results. Both approaches demonstrate that the holes have a tendency to pair in p-and d-wave channels at realistic values of t/J. Interactions leading to pairing and effects selecting p and d waves are thoroughly investigated. The role of transverse spin fluctuations is considered using perturbation theory. Based on the results of the present study, we discuss the pairing problem in the realistic t-J-like model. Possible implications for preformed pairs formation and phase separation are drawn. ͓S0163-1829͑99͒04127-2͔

We report on a detailed examination of numerical results and analytical calculations devoted to a study of two holes doped into a two-dimensional, square lattice described by the t-J model. Our exact diagonalization numerical results represent the first solution of the exact ground state of two holes in a 32-site lattice. Using this wave function, we have calculated several important correlation functions, notably the electron momentum distribution function and the hole-hole spatial correlation function. Further, by studying similar quantities on smaller lattices, we have managed to perform a finite-size scaling analysis. We have augmented this work by endeavouring to compare these results to the predictions of analytical work for two holes moving in an infinite lattice. This analysis relies on the canonical transformation approach formulated recently for the t-J model. From this comparison we find excellent correspondence between our numerical data and our analytical calculations. We believe that this agreement is an important step helping to justify the quasiparticle Hamiltonian, and, in particular, the quasiparticle interactions that result from the canonical transformation approach. Also, the analytical work allows us to critique the finite-size scaling ansatzes used in our analysis of the numerical data. One important feature that we can infer from this successful comparison involves the role of higher harmonics in the two-particle, d-wave symmetry bound state-the conventional ͓cos(k x )Ϫcos(k y )͔ term is only one of many important contributions to the d-wave symmetry pair wave function. ͓S0163-1829͑98͒04044-2͔