Extremely Correlated Quantum Liquids

The Extremely Correlated Quantum Liquid (ECQL) is obtained in the $U\rightarrow \infty$ limit of strongly correlated systems- so that double occupancy is prohibited[1]. The $t$-$J$ model, a standard example of this class is studied by the new formulation[1]. We present the exact Schwinger Dyson equation for its Greens function, in terms of singlet and triplet vertex functions. The vertices are expanded further in a set of non linear equations, and the existence of a low hole density expansion is demonstrated. Its Fermi surface volume differs from the Luttinger Ward volume {\em at all densities}. The excitations are fractionally charged particles, where the fraction is determined by the density. The fractionalization arises from a modified Pauli principle for filling of the Lower Hubbard band. Numerical results for the magnetic susceptibility and the spectral functions arising from systematic expansions are presented elsewhere in this conference [2-3]. [1] {\em Extremely Correlated Quantum Liquids}, B. S. Shastry Preprint (2009). [2] {\em Magnetic response of the Extremely Correlated Electron Liquid}, A. Garg, D. Hansen and B. S. Shastry (APS March meeting 2010). [3] {\em Spectral functions of the Extremely Correlated Quantum Liquid}, D. Hansen, A. Garg, and B. S. Shastry (APS March meeting 2010).