Conserving Approximations for Strongly Correlated Electron Systems: Bethe-Salpeter Equation and Dynamics for the Two-Dimensional Hubbard Model

In this Letter we describe a new technique for investigating phase transitions and dynamics in interacting electron systems. This technique is based on the derivation and self-consistent solution of infinite-order conserving approximations. It provides a new approach to the study of two-particle correlations with strong frequency and momentum dependence. We use this technique to derive a low-temperature phase diagram and dynamic correlation functions for the two-dimensional Hubbard model.