Variational Study of the Spin-Gap Phase of the One-Dimensional t-J Model

TL;DR

This paper introduces a variational wave function with a Jastrow factor to accurately describe the spin-gap phase in the one-dimensional t-J model, establishing a link between variational parameters and Luttinger liquid properties.

Contribution

The study develops a correlated wave function approach that captures the spin-gap phase and relates variational parameters to fundamental Luttinger liquid exponents.

Findings

The wave function correctly describes the long-range behavior of the Luther-Emery phase.

A relation between the Jastrow parameter and the Luttinger exponent is established.

Variational Monte Carlo confirms the effectiveness of the proposed approach.

Abstract

We propose a correlated spin-singlet-pairs wave function to describe the spin-gap phase of the one-dimensional $t-J$ model at low density. Adding a Jastrow factor with a variational parameter, $\nu$, first introduced by Hellberg and Mele, is shown to correctly describe the long-range behavior expected for the Luther-Emery phase. Using the variational Monte Carlo method we establish a relation between $\nu$ and the Luttinger exponent $K_\rho$, $K_\rho=\frac{1}{2\nu}$.