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Modern Physics Letters B

A VARIATIONAL STUDY OF FERMI AND LUTTINGER LIQUID WAVEFUNCTIONS IN THE TWO-DIMENSIONAL t-J MODEL

Franjo Franjic, Sandro Sorella

Published Aug 10, 1996• 4 citations
Publisher

Abstract

Using a recently developed technique, we determine the Jastrow potential of the variational wavefunction for the two-dimensional t-J model. This wavefunction describes a Fermi liquid ground state and is compared with the Luttinger liquid wavefunction used by Gros and Valentí. Estimates of the energy of these states are calculated using the variational Monte Carlo technique, showing that the Fermi liquid state has a little power energy.

DOI
10.1142/s0217984996000997

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Using a recently developed technique, we determine the Jastrow potential of the variational wavefunction for the two-dimensional t-J model. This wavefunction describes a Fermi liquid ground state and is compared with the Luttinger liquid wavefunction used by Gros and Valentí. Estimates of the energy of these states are calculated using the variational Monte Carlo technique, showing that the Fermi liquid state has a little power energy.
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.
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Excitations of the two-dimensional electron gas, including many-body effects, are calculated with a variational Monte Carlo method. Correlated sampling is introduced to calculate small energy differences between different excitations. The usual pair-product (Slater-Jastrow) trial wave function is found to lack certain correlations entirely so that backflow correlation is crucial. From the excitation energies calculated here, we determine Fermi-liquid parameters and related physical quantities such as the effective mass and the Land\'e g factor of the system. Our results for the effective mass are compared with previous analytic calculations.
We present very general techniques for investigating strongly correlated lattice fermions in one dimension. We derive a variational wave function with a long ranged Jastrow factor that automatically satisfies the no double occupancy constraint present in many model Hamiltonians. The wave function is shown to be a generalized Luttinger liquid, and we use it to estimate ground state properties of the strongly correlated Hubbard model and the t-J model. We develop a numerical method to project the ground state from an arbitrary trial state. With the Luttinger liquid wave function as the initial guess, we calculate the exact ground state phase diagram of the t-J model. We discover a new phase in the model where Luttinger liquid behavior breaks down and superconducting correlations dominate the long range behavior of the system.
The spin, charge and pairing correlation functions for the ground state of two-dimensional t−Jt-Jt−J model are calculated by using the power method which projects out the ground state from a variational wave function. ``Exact'' results are obtained for 10×1010\times1010×10 and 8×88\times88×8 lattices with low particle densities. The results are surprisingly similar to that of one-dimensional t−Jt-Jt−J model. The phenomenology is almost perfectly correlated with the concept of Tomonaga-Luttinger liquid and it is incompatible with traditional Fermi liquid theory.