Variational Wavefunction Monte Carlo on Two-Dimensional Lattices

Sunita Kannan, Courtney Lannert

Stephen Fahy

Biao Hao, Wei‐Guo Yin, Chang-De Gong

We present a spin- antiferromagnetic Reisenberg model in an interacting boson representation exactly by using modified Holstein–Primakoff transformation. For interacting boson systems on one-dimensional linear chains and square lattices, we perform Monte–Carlo calculations using the well-established Jastrow-type trial wavefunction. We find that the ground state energies and spin correlations agree well with other numerical and theoretical results.

Jan Tobochnik, G. G. Batrouni, Harvey Gould

Klaus Mølmer, Yvan Castin

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.