Luttinger liquid instability of the 2Dt-Jmodel: A variational study

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Abstract
We study variationally the possible occurrence of a Luttinger liquid in the normal state of the 2D t-J model. For this, we generalize to 2D a Luttinger-Jastrow-Gutzwiller-type wave function introduced by Hellberg and Mele for the 1D t-J model. We show that this wave function does show also in 2D the characteristic correlations of a Luttinger liquid and the gains in kinetic energy stabilize the Luttinger liquid state with respect to Fermi liquid states with short-range correlations only. In addition, we provide rigorous lower bounds to the transition to the fully phase separated state at larger ratios J/t.