Extremely Correlated Fermi Liquids

We present the theory of an extremely correlated Fermi liquid with $U\to \infty$. This liquid has an underlying auxiliary Fermi liquid Green’s function that is further caparisoned by extreme correlations. The theory leads to two parallel hierarchies of equations that permit iterative approximations in a certain parameter. Preliminary results for the spectral functions display a broad background and a distinct $T$ dependent left skew. An important energy scale $\Delta (\overrightarrow{k},x)$ emerges as the average inelasticity of the FL Green’s function, and influences the photoemission spectra profoundly. A duality is identified wherein a loss of coherence of the ECFL results from an excessively sharp FL.

Figure 1

The density $n=.85$ and ${\omega }_0=0.25$. From left to right ${\rho }_{\mathcal{G}}(x)$ for energies (in units of W) $\xi =-0.3$, $-0.2$, $-0.1$, 0.,0.05 for both the FL (dashed) and the ECFL(solid) theories. Inset in (A): provides an enlarged view of the $\xi =-0.1$ plots after inversion, and displays the left-skew asymmetry of the ECFL spectrum relative to the FL. Inset in (B) shows the DC resistivity $\rho (T)$ within a bubble approximation as a function of $T$ for the FL (blue) and the ECFL (red). Because of spectral redistribution, the ECFL reaches linear $T$ behavior at a lower $T$ than the FL.