Using computational techniques, it is shown that pairing is a robust property of hole doped antiferromagnetic (AF) insulators. In one dimension (1D) and for two-leg ladder systems, a BCS-like variational wave function with long-bond spin-singlets and a Jastrow factor provides an accurate representation of the ground state of the t-J model, even though strong quantum fluctuations destroy the off-diagonal superconducting (SC) long-range order in this case. However, in two dimensions (2D) it is argued -and numerically confirmed using several techniques, especially quantum Monte Carlo (QMC) -that quantum fluctuations are not strong enough to suppress superconductivity. 74.20.Mn, 71.10.Fd, 71.10.Pm, 71.27.+a The nature of high temperature superconductors remains an important unsolved problem in condensed matter physics. Strong electronic correlations are widely believed to be crucial for the understanding of these materials. Among the several proposed theories are those where antiferromagnetism induces pairing in the d x 2 −y 2 channel [1]. These approaches include the following two classes: (i) theories based on Resonant Valence Bond (RVB) wave functions, with electrons paired in long spin singlets in all possible arrangements [2,3], and (ii) theories based on two-hole d x 2 −y 2 bound states at infinitesimal doping, formed to minimize the damage of individual holes to the AF order parameter, which condense at finite pair density into a superconductor [4]. However, recent density matrix renormalization group (DMRG) calculations have seriously questioned these approaches since non-SC striped ground states were reported for realistic couplings and densities in the t-J model [5]. Clearly to make progress in the understanding of copper oxides, the 2D t-J model ground state must be fully understood, to distinguish among the many proposals.In this paper, using a variety of powerful numerical techniques, the properties of the t-J model are investigated. Our main result is that in the realistic regime of couplings the 2D t-J model supports a d x 2 −y 2 SC ground state, confirming theories of Cu-oxides based on AF correlations. The t-J model used here is. . stands for nearestneighbor sites, and n i and S i are the electron density and spin at site i, respectively. Our study focuses on the low hole-doping region of chains, two-leg ladders, and square clusters, using different numerical techniques: QMC (pure variational and fixed-node (FN) approximations), DMRG, and Lanczos. Within our QMC approach, it is possible to further improve the variational and FN accuracy by applying a few (p ≤ 2) Lanczos steps to the variational (p = 0) wave function |Ψ V ,. Non-variational estimates of energy and correlation functions can also be extracted with the variance-extrapolation method [6].Our BCS variational wave function is defined as

We report 115 In and 59 Co Nuclear Magnetic Resonance (NMR) measurements in the heavy fermion superconductor CeCoIn5 above and below Tc. The hyperfine couplings of the 115 In and 59 Co are anisotropic and exhibit dramatic changes below 50K due to changes in the crystal field level populations of the Ce ions. Below Tc the spin susceptibility is suppressed, indicating singlet pairing. PACS Numbers: 74.70.Tx, 76.60.Cq In heavy fermion systems the interplay of magnetism and superconductivity gives rise to a diverse range of ground states including an unconventional form of superconductivity. The recently discovered family of heavy fermion compounds CeMIn 5 , where M = Co, Rh or Ir exemplifies these effects. Whereas the Rh compound undergoes a transition from antiferromagnetic to superconducting under pressure [1], the Ir [2] and Co [3] compounds superconduct at ambient pressure, with the Co system exhibiting the highest known transition temperature (2.3K) for any heavy fermion system. Evidence from heat capacity, thermal transport and µSR indicate that the pairing symmetry in the superconducting state is unconventional and that there are line nodes in the superconducting gap. [4,5] The bulk magnetic susceptibility, χ, of tetragonal CeMIn 5 displays systematic trends consistent with the diversity of observed ground states. In all three cases χ is anisotropic, and is largest for field applied along the c direction. In the ab plane, χ ab is essentially the same for all three materials. However, χ c exhibits a maximum at ∼ 10 K for CeRhIn 5 (T N = 3.8 K), whereas for the superconductors CeIrIn 5 and CeCoIn 5 χ c diverges at low temperatures until T c is reached. For both of these materials χ c also exhibits a plateau-like feature around 50 K, which is less pronounced for the Ir system. The origin of this feature and the relationship between χ c and T c have been sources of debate, however both the plateau and the divergence are intrinsic and independent of field.[3]Here we report a detailed study of site-specific magnetic shifts in CeCoIn 5 using nuclear magnetic resonance (NMR). Measurements in the normal state provide a microscopic measure of the local susceptibility and we find anomalous temperature dependencies. This behavior is likely due to the thermal depopulation of a crystal field (CEF) excitation of the Ce ions. We find remarkably strong departures from the expected proportionality between bulk susceptibility and the NMR Knight shift. We will argue that this effect is indicative of a high degree Ce moment localization, a feature that may play a role in the mechanism for superconductivity in this material. In the superconducting state the temperature dependencies of the shifts reveal a suppression of the spin susceptibility consistent with spin-singlet pairing.Crystals of CeCoIn 5 were grown from an In flux as described in [3]. The tetragonal crystal structure of CeCoIn 5 consists of alternating layers of CeIn 3 and CoIn 2 and so has two inequivalent In sites per unit cell. The In(1) site has axial symmetry ...

The local enhancement of antiferromagnetic correlations near vacancies observed in a variety of spin systems is analyzed in a single framework. Variational calculations suggest that the resonatingvalence-bond character of the spin correlations at short distances is responsible for the enhancement. Numerical results for uniform spin chains, with and without frustration, dimerized chains, ladders, and two dimensional clusters are in agreement with our conjecture. This short distance phenomenon occurs independently of the long distance behavior of the spin correlations in the undoped system. Experimental predictions for a variety of compounds are briefly discussed.PACS numbers: 64.70. Kb,75.10.Jm,75.50.Ee Studies of ladder compounds continue producing fascinating results. In addition to the discovery of a spin gap in undoped even-leg ladders [1], superconductivity at high pressure in Sr 0.4 Ca 13.6 Cu 24 O 41.84 , with 2-leg ladders and chains in its structure, has been recently reported [2]. Both properties, predicted by theoretical arguments, [3] indicate a close interplay between the spin and charge degrees of freedom leading to a rich phase diagram. More recently, the doping of ladders with nonmagnetic impurities (replacing spin 1/2 Cu 2+ by spin 0 Zn 2+ ) has revealed another surprising property: the spin gap is rapidly suppressed as the Zn concentration increases, and an antiferromagnetic (AF) phase is stabilized [4]. A similar behavior has also been observed in spin-Peierls chains [5], which have a spin gap produced by dimerization. The phenomenon is interesting since a spin ordered state is generated by the random replacement of spins by vacancies, an apparently disordering procedure. These results have been recently addressed with one dimensional (1D) spin models using field theory [6] and numerical techniques. Computational studies found that the AF correlations near a vacancy in dimerized chains [7] and 2-leg ladders [7,8] are enhanced with respect to the undoped case. It was conjectured that this local enhancement may trigger the 3D AF order in Zn-doped dimerized chains and ladders. In-gap weakly interacting S = 1/2 localized states were found near Zn [9]. However, the microscopic origin of the local AF enhancement near a vacancy is still not intuitively understood.Independently of these recent developments, related phenomena have been discussed in a variety of contexts: 1. A staggered moment appears near a vacancy for 1D S = 1 Heisenberg systems [10]; 2. The undimerized 1D S = 1/2 Heisenberg model has an enhanced spin structure factor S(π) near vacancies according to boundary conformal field theory and Monte Carlo (MC) simulations [11]; 3. Near a vacancy injected into a 2D Néel ordered state, the staggered moment increases with respect to the undoped system [12].In this paper it is proposed that all these examples of locally enhanced antiferromagnetism near a vacancy, which have been studied independently in the literature, may have a simple common explanation. The unifying picture relies on the res...