What is the nature of the excitations (and one-electron Greens function) of the Hubbard model in the infinite-U limit and for large dopings (perhaps x greater than 0.3) above which superconductivity occurs?

Anderson claims:

- the strong interactions lead to a significant particle-hole asymmetry [which should be visible in tunneling spectra]
- excitations exhibit anomalous forward scattering
- the quasi-particle weight Z vanishes on the Fermi surface

- there is a formal similarity of this problem with that of Fermi-edge singularities in the X-ray spectra of metals, where the one-electron Greens function has a power law decay associated with the phase shift from an infinite potential.

- A simple argument (exploiting the Friedel sum rule) gives the main quantitative prediction of the theory a value for the doping (x) dependence of the exponent

- a power-law frequency dependence of the optical conductivity
- this theory may have some similarities to one of Norman and Chubukov.
- Quasiparticles emerge in the superconducting and pseudogap states: "But above T* and above the gap energy the quasiparticles experience power-law decay: essentially,
**the line of quasiparticle poles turns into a cut in the complex plane**."

Hi Ross,

ReplyDeleteIt's my understanding that allowing for finite mass (dispersion) of the scatterer in the X-ray edge problem cuts off the divergences giving rise to orthogonality and restores a finite residue.

See for instance "The effect of recoil on edge singularities", P. Nozières J. Phys. I France 4 (1994) 1275-1280