A partial charge-spin separation fermion-spin theory is developed to study the normal-state properties of the underdoped cuprates. In this approach, the physical electron is decoupled as a gauge invariant dressed holon and spinon, with the dressed holon behaving like a spinful fermion, representing the charge degree of freedom together with the phase part of the spin degree of freedom, while the dressed spinon is a hard-core boson, representing the amplitude part of the spin degree of freedom. The electron local constraint for the single occupancy is satisfied. Within this approach, the charge and spin dynamics of the underdoped cuprates are studied based on the t-t ′ -J model. It is shown that the charge dynamics is mainly governed by the scattering from the dressed holons due to the dressed spinon fluctuation, while the scattering from the dressed spinons due to the dressed holon fluctuation dominates the spin dynamics. 74.25.Fy, 74.25.Ha,

We used a quantum Monte Carlo method to study the magnetic impurity adatoms on graphene. We found that by tuning the chemical potential we could switch the values of the impurity's local magnet moment between relatively large and small values. Our computations of the impurity's spectral density found its behavior to differ significantly from that of an impurity in a normal metal and our computations of the charge-charge and spin-spin correlations between the impurity and the conduction band electrons found them to be strongly suppressed. In general our results are consistent with those from poor man's scaling and numerical renormalization group methods.

Within the kinetic energy driven superconducting mechanism, the magnetic nature of cuprate superconductors is discussed. It is shown that the superconducting state is controlled by both charge carrier gap function and quasiparticle coherent weight. This quasiparticle coherent weight grows linearly with the hole doping concentration in the underdoped and optimally doped regimes, and then decreases with doping in the overdoped regime, which leads to that the maximal superconducting transition temperature occurs around the optimal doping, and then decreases in both underdoped and overdoped regimes. Within this framework, we calculate the dynamical spin structure factor of cuprate superconductors, and reproduce all main features of inelastic neutron scattering experiments, including the energy dependence of the incommensurate magnetic scattering at both low and high energies and commensurate resonance at intermediate energy. 74.20.Mn, 74.25.Ha, 74.62.Dh

To address the issue of electron correlation driven superconductivity in graphene, we perform a systematic quantum Monte Carlo study of the pairing correlation in the t − U − V Hubbard model on a honeycomb lattice. For V = 0 and close to half filling, we find that pairing with d + id (d x 2 −y 2 + id ′ xy in its specific form) symmetry dominates pairing with extended-s symmetry. However, as the system size or the on-site Coulomb interaction increases, the long-range part of the d + id pairing correlation decreases and tends to vanish in the thermodynamic limit. An inclusion of nearest-neighbor interaction V , either repulsive or attractive, has a small effect on the extended-s pairing correlation, but strongly suppresses the d + id pairing correlation.Recently, graphene has attracted the attention of experimentalists and theorists [1][2][3][4] . One of the most intriguing properties of graphene is that its chemical potential can be tuned through an electric field effect, and hence it is possible to change the type of carriers, electrons, or holes, opening the doors for carbon based electronics 2,5,6 . Doped graphene has a finite density of state at the chemical potential, which, in combination with pronounced antiferromagnetic (AFM) spin fluctuations close to half filling 7,8 , may lead to an unconventional superconductivity. Experimentally, superconducting (SC) states in graphene have been realized by the proximity effect through contact with SC electrodes 9 , which indicates that Cooper pairs can propagate coherently in graphene. These facts raise the question as to whether it would be possible to modify graphene to be an intrinsic superconductor.Various theoretical attempts 10-15 have been made to understand the superconductivity in graphene. Uchoa et al.10 suggested that an extended-s (ES) SC phase may be realized at the mean-field level due to the special structure of the honeycomb lattice. On the other hand, in a weak-coupling functional renormalization group study 12 , Honerkamp found that with a nearest-neighbor (NN) spin-spin interaction J, doping away from half filling can lead to a d + id SC state, which is similar to the SC state on the triangular lattice 16,17 . This d + id SC state was also found to be stable in a mean-field study 13 of a phenomenological Hamiltonian 14 . Recent variational Monte Carlo simulations of the repulsive Hubbard model provide further support for the d + id SC state 15 . Although the results based on mean-field theory and other approximate methods are encouraging, it is far from certain that there exists a SC ground state in the physical parameter region of graphene. It is well known that the low energy properties of graphene can be described by the two-dimensional Hubbard model on a honeycomb lattice 1 . In graphene, the on-site Hubbard repulsion is approximately half the band width, and this places graphene in an intermediate-coupling regime. Thus, it is questionable to approach the effect of electron correlations in graphene from either a weak-coupling or strongcoupling...