Strong Coupling Expansions for Models of Strongly Correlated Electrons

Ohio State University Research Foundation -Do Not Use, Columbus OH

Investigators

Abstract

The properties of strongly correlated electrons in reduced dimensions remain some of the most fascinating problems in condensed matter physics. The discovery of high temperature superconductivity focused attention on two-dimensional models, with the copper oxide plane found in high temperature superconductors well described by a square lattice. The central theoretical hypothesis of research in high temperature superconductivity is that strong electronic correlations in reduced dimensions lead to enhanced superconducting correlations when the electrons are itinerant. A corollary of this hypothesis is that the low energy excitations in high temperature superconductors are anomalous due to strong correlations. Exactly how strong correlations produce these effects for two-dimensional systems, if at all, is currently not known. This research will study the effects of strong correlations and reduced dimensionality on systems of itinerant electrons by calculating high temperature series for correlation functions of the 2D t-J model. The 2D t-J model has been widely adopted as the fundamental model for high temperature superconductors. Direct numerical results are needed to sort through approximate analytic treatments of 2D strongly correlated electrons. High temperature series provide a means to obtain accurate, unbiased results in the thermodynamic limit for key properties of the 2D t-J model. The specific quantities to be calculated are thermodynamic properties, equal time correlation functions and zero frequency susceptibilities. The strength of superconducting correlations in the 2D t-J model are of key interest for applications to high temperature superconductivity. Series will be calculated for all possible symmetries of spin singlet pairing correlations. The full range of doping will be considered, from pseudogap behavior at small doping to the crossover to more conventional behavior at large doping. The zero frequency, wave vector dependent charge susceptibility will be used to search for charge stripe formation, while the zero frequency, wave vector dependent spin susceptibility will aid interpretation of NMR experiments. Equal time correlation functions and susceptibilities through their temperature derivatives can both be used to determine the momentum dependence of the low energy spin and charge excitations of the 2D t-J model. All quantities calculated for the full 2D square lattice will also be calculated for ladder lattices and other subsets of the square lattice with varying boundary conditions. This will allow a detailed study of boundary effects for systems of strongly correlated electrons. The series results will also be compared to density matrix renormalization group calculations on the same lattices and with the same boundary conditions. %%% Theoretical computational research will be conducted on a model for the behavior of electrons in the high temperature superconductors. The results will aid in understanding these intriguing, fundamental and potentially useful materials. ***