Abstract

We model lightly doped cuprate superconductors by extended t - J model. It is shown that
the spin liquid phase is driven by quantum fluctuations related to Lifshitz transition between the
collinear Neel state and the incommensurate spin spiral phase. We derive generic zero temperature
phase diagram that includes all three phases, (i) Neel, (ii) Algebraic Spin Liquid, (iii) Static spin
spiral. We argue that physical cuprates correspond to the Algebraic Spin Liquid phase and, in some
cases, to the border line between the Spin liquid and the Static spin spiral. We also show that the
magnetic dispersion observed in neutron scattering depends on degree of magnetic overcriticality
and some other parameters. These details give rise to the differences between the hour-glass and the wine-glass dispersions, and between the "short leg"and "long leg" hour-glasses observed in different
compounds.

Y. A. Kharkov1 and O. P. Sushkov1
1 School of Physics, University of New South Wales, Sydney 2052, Australia
(Dated: May 25, 2018)