Spin Fluctuations in an Itinerant Heisenberg System: Naive Rpa Treatment

The dynamical spin fluctuations in a two-dimensional square lattice in its paramagnetic phase are examined within the framework of Random Phase Approximation(RPA). Itinerant carriers with spin interact with each other via an antiferromagnetic Heisenberg interaction. Then there appear three fundamental scattering processes;a) scattering between parallel spins,b) scattering between antiparallel spins and c) scattering with spin-flip. To examine how these scattering processes affect the dynamical spin fluctuations, we pick up carefully all possible combination of RPA diagrams in a consistent manner and take the spin rotational symmetry into account. Then it becomes clear that we have to take up a sequence of the irreducible single loop which in itself is modified due to the particle-hole ladder type vertex correction.We set up the Bethe-Salpeter equation for the vertex correction and show that this can be solved in a closed form due to separable nature of the antiferromagnetic interaction. We evaluated numerically the effectof the vertex correction and found that the correction is negligibly small. Therefore we propose that in an itinerant Heisenberg system, including the $t$-$J$ model as its derivertive, the simplified RPA, where the irreducible single loop is unrenormalized, works very well. This conclusion strongly support the simplified treatment which is widely used in High-$T_{c}$ problem. Moreover the present formalism enables us to proceed further microscopic calculations on the magnetic properties in the current High-$T_{c}$ problem.Comment: 16 pages,latex, figures available upon request ([email protected]). Accepted for publication in Prog.Theo.Phys. Vol94(1995, Oct.

Superconductivity of Carriers Doped into the Static Charge Density Wave State in 2-Dimensional Square Lattice

On the purpose of studying the effect of long-range Coulomb-interaction in strongly correlated electronic systems we bring in as its representative the nearest-neighbor repulsion ($v$) in addition to the on-site repulsion ($u$) and shall investigate the possibility of the superconducting transition of carriers doped into the charge-density wave (CDW) state expected for $v\,>\,u/4$ in 2-dimensional square lattice. We shall see that strongly correlated hopping processes of doped carriers make the systems superconducting. The favored superconducting phase is of extended s-wave symmetry, and $T_{c} \sim$100K is shown to easily be attained near the half-filling.Comment: 26 pages, Tex, 10 figures (available upon request [email protected]

Spin Fluctuations in Magnetically Coupled Bi-layer Cuprates

We propose a possible mechanism of pseudo spin gap anomaly(PSGA) in magnetically coupled bi-layer cuprates without any fermion pairing instability. In our proposal PSGA does not necessarily require the spin-charge separation or the breakdown of the Fermi liquid description of a normal state of the cuprate superconductor.The low energy magnetic excitations are mainly governed by the {\it itinerant nature of the intra-layer system} and {\it the inter-layer antiferromagnetic coupling}. No matter how weak the bare inter-layer coupling is, it can be dramatically enhanced due to the intra-layerspin fluctuations. As the temperature decreases near the antiferromagnetic phase boundary the strongly enhanced inter-layer correlation induces the inter-layer particle-hole exchange scattering processes that tend to enhance the inter-layer spin singlet formation and kill the triplet formation. We propose that the coupling of spin fluctuations on the adjacend layers via the strong repulsive interaction between parallel spins travelling on each layer give rise to the dynamical screening effects. As a result the low energy part of the spin excitation spectrum is strongly suppressed as the temperature decreases near the antiferromagnetic phase boundary. We ascribe PSGA to this dynamical screening effects.Comment: 30 page, latex, figures are available upon reques