Luttinger-Liquid Behaviour in 2D: The Variational Approach

Fedor Vasilievich Kusmartsev, Alan H. Luther, A. A. Nersesyan

Stefano Bellucci A, Pasquale Onorato

Claudius Gros, Roser Valentí

We study a variational formulation of the Luttinger-liquid concept in two dimensions. We show that a Luttinger-liquid wavefunction with an algebraic singularity at the Fermiedge is given by a Jastrow-Gutzwiller type wavefunction, which we evaluate by variational Monte Carlo for lattices with up to 38 × 38 = 1444 sites. We therefore find that, from a variational point of view, the concept of a Luttinger liquid is well defined even in 2D. We also find that the Luttinger liquid state is energetically favoured by the projected kinetic energy in the context of the 2D t-J model. We study and find coexistence of d-wave superconductivity and Luttinger-liquid behaviour in two-dimensional projected wavefunctions. We then argue that generally, any two-dimensional d-wave superconductor should be unstable against Luttinger-liquid type correlations along the (quasi-1D) nodes of the d-wave order parameter, at temperatures small compared to the gap.

Roser Valentí, Claudius Gros

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.

Matthew P. A. Fisher, L. I. Glazman

Roser Valentí, Claudius Gros

In Eq. (3) a minus sign was missing in the exponent.It should read r