Possible Exotic Phases in the One-Dimensional Extended Hubbard Model

We investigate numerically the ground state phase diagram of the one-dimensional extended Hubbard model, including an on--site interaction U and a nearest--neighbor interaction V. We focus on the ground state phases of the model in the V >> U region, where previous studies have suggested the possibility of dominant superconducting pairing fluctuations before the system phase separates at a critical value V=V_PS. Using quantum Monte Carlo methods on lattices much larger than in previous Lanczos diagonalization studies, we determine the boundary of phase separation, the Luttinger Liquid correlation exponent K_rho, and other correlation functions in this region. We find that phase separation occurs for V significantly smaller than previously reported. In addition, for negative U, we find that a uniform state re-enters from phase separation as the electron density is increased towards half filling. For V < V_PS, our results show that superconducting fluctuations are not dominant. The system behaves asymptotically as a Luttinger Liquid with K_rho < 1, but we also find strong low-energy (but gapped) charge-density fluctuations at a momentum not expected for a standard Luttinger Liquid.

The United Methodist Church at 40: What Can We Hope For?

The necessity we face for the future of Methodism is the re-invention of traditions. To re-invent traditions is to re-visit the past with all of its richness; to discern what in our tradition is most central to Christian faith; to analyze those parts of our past that continue to give life; to discern and build upon what is of value in the newly emerging tradition; and to reflect on those aspects of the neglected and rejected past that challenge our present perspectives and practices. To re-invent traditions is to develop new perspectives and practices from the building blocks of the past and from the fresh movements of the Spirit in the present. To do so is to recognize that Christianity in general, and Methodism in particular, is marked by traditions that have continually been passed on, critiqued, eliminated, created, and re-invented for the sake of a living Christian witness. What we can hope for is that God is there in the future already, pulling us toward God’s own New Creation.