Strongly-correlated Systems Research Articles

Local dynamics and strong correlation physics: One- and two-dimensional half-filled Hubbard models

We report on a non-perturbative approach to the 1D and 2D Hubbard models that is capable of recovering both strong and weak-coupling limits. We first show that even when the on-site Coulomb repulsion, U, is much smaller than the bandwith, the Mott-Hubbard gap never closes at half-filling in both 1D and 2D. Consequently, the Hubbard model at half-filling is always in the strong-coupling non-perturbative regime. For both large and small U, we find that the population of nearest-neighbour singlet states approaches a value of order unity as $T\to 0$ as would be expected for antiferromagnetic order. We also find that the double occupancy is a smooth monotonic function of U and approaches the anticipated non-interacting limit and large U limits. Finally, in our results for the heat capacity in 1D differ by no more than 1% from the Bethe ansatz predictions. In addition, we find that in 2D, the heat capacity vs T for different values of U exhibits a universal crossing point at two characteristic temperatures as is seen experimentally in a wide range of strongly-correlated systems such as $^3He$, $UBe_3$, and $CeCu_{6-x}Al_x$. The success of this method in recovering well-established results that stem fundamentally from the Coulomb interaction suggests that local dynamics are at the heart of the physics of strongly correlated systems.

I. First Principles Cluster Calculations for the Electronic Structures of CuO7 Octahedron and CuO5 Pyramid

In this paper we first describe the multi-configuration self-consistent field method with configuration interaction (MCSCF-CI) which is a variational method most suitable for strongly-correlated cluster systems. Then the calculated results of CuO 6 cluster embedded in hole-doped La 2-x Sr x CuO 4 and of CuO 4 cluster in the electron-doped Nd 2-x Ce x CuO 4 are reviewed. Finally the calculated results on the electronic structure of CuO 5 pyramid embedded in the insulating YBa 2 Cu 3 O 6 and superconducting YBa2Cu3O7 are newly presented. In the latter case we will clarify an important role of the Cu-O chain in the electronic and superconducting state of YBa2Cu3O7 .

Anyon superconductivity in strongly-correlated spin systems

The present state of the gauge theory of high-temperature superconductivity in strongly-correlated two-dimensional spin systems is reviewed. Basic ideas on the statistics of elementary excitations in spatially two-dimensional systems are presented and are used in an analysis of the structure of the energy spectrum and the form of the wave function of a set of anyon quasiparticles in both the long-wave continuous and lattice limits. The continuous and lattice theories are used to classify the phase states, and the hierarchy of phase transitions is described in terms of the topological quantum field theory. Thermodynamic and electrodynamic properties of anyon systems are described, and the experimental consequences of the Chern–Simons theory of high-Tc superconductivity are discussed.

Анионная сверхпроводимость в сильно коррелированных спиновых системах

Анионная сверхпроводимость в сильно коррелированных спиновых системах

A simulated annealing based algorithm for eigenvalue problems

We present a simple, iterative algorithm to find the lowest (few) eigenvalue(s) and eigenvector(s) of a large sparse real Hermitian matrix. The algorithm is an application of the simulated annealing technique implemented via molecular dynamics. We also demonstrate that the slow rate of convergence, characteristic of the late-time behaviour of such annealing based methods, can be considerably improved by using simple gradient minimization schemes. Our studies are based on a large number of real Hermitian matrices of dimensions up to 15876 arising out of our investigations of strongly-correlated systems using the finite-cluster approach. We also investigate the effect of the controlling parameters (time step and fictitious mass) on the convergence and suggest a way to choose these parameters a priori.

High-T c superconductors as almost-localized systems: Resonance and fluctuations

A new approach is developed to treat the Mott localisation in strongly-correlated systems. It is based on a perturbation theory on the Hubbard model as a function of the superexchange coupling J. The Hartree term which is proved to correspond to the Gutzwiller approximation constitutes the natural ground state around which the system fluctuates. It is shown how superconductivity arises from intersite correlations developed by quantum fluctuations around a re resonant state.

Superconductivity and Mott localization

A new approach is developed to treat the Mott localization in strongly-correlated systems. It is based on a constrained perturbation theory of the Hubbard model as a function of the superexchange coupling J. The Hartree term which is proved to correspond to the Gutzwiller approximation constitutes the natural ground state around which the system fluctuates. We interpret it in terms of a resonance in complete analogy with the Abriskov-Suhl resonance of the Kondo problem. It is shown how superconductivity is induced by quantum fluctuations around this resonant state.