1207.6826 (B. Sriram Shastry)

Extremely Correlated Fermi Liquids: The Formalism    [PDF]

B. Sriram Shastry

We present the detailed formalism of the extremely correlated Fermi liquid theory developed for treating the physics of the t-J model. We start from the exact Schwinger equation of motion for the Greens function for projected electrons, and develop a procedure by which this is expanded systematically in a parameter $\lambda$, relating to the double occupancy. The resulting Greens function has a canonical part arising from an effective Hamiltonian of the auxiliary electrons, and a caparison part, playing the role of a frequency dependent adaptive spectral weight. This adaptive weight balances the requirement at low $\omega$, of the invariance of the Fermi volume, and at high $\omega$ of decaying as $\frac{c_0}{i \omega}$, with a correlation depleted $c_0 <1$. The effective Hamiltonian describing the auxiliary Fermions is given a natural interpretation with an effective interaction $V_{eff}$ containing both the exchange $J_{ij}$, and the hopping parameters $t_{ij}$. Simple but important {\em shift invariances} of the t-J model are noted with respect to translating its parameters uniformly. These play a crucial role in constraining the form of $V_{eff}$ and also provide checks for further approximations. The auxiliary and physical Greens function satisfy two sum rules, and the Lagrange multipliers for these are identified. A complete and explicitly set of equations for the Greens functions to second order in $\lambda$ is given, satisfying various invariances. A systematic iterative procedure for higher order approximations is detailed. A superconducting instability of the theory is noted at the simplest level, leading to d-wave order unambiguously, with a high transition temperature.

View original: http://arxiv.org/abs/1207.6826