The Luttinger Sum Rule in Doped Spin Liquids With some speculations about the Pseudogap Phase of the Underdoped Cuprates

摘要

The Luttinger sum rule is usually considered for Landau Fermi liquids in which the single particle Green's function G(k, 0) changes sign at the the Fermi surface by passing through infinity. However the general proof allows also for a sign change at which G has a zero. A recent analysis by Konik and coworkers considers a model of 2-leg Hubbard ladders weakly coupled by a small long range interladder tunneling. At half-filling a semimetallic state with small Fermi pockets is induced beyond a threshold tunneling strength. The sign changes in G(k, 0) relevent for the Luttinger sum rule now take place at surfaces with both zeros and infinities. The zero surfaces differ from the minimum gap surfaces. The latter are often used in ARPES experiments on underdoped cuprates to obtain an underlying Fermi surface but this procedure leads to problems with the Luttinger sum rule. Some speculations on how the Luttinger sum rule should be applied to the pseudogap phase of the underdoped cuprates are included.