Variational study of the one dimensional t-J model

TL;DR

This paper investigates the one-dimensional t-J model using variational wave functions, identifying limitations of the Gutzwiller wave function and proposing a Pfaffian wave function that accurately captures the phase diagram and correlations.

Contribution

It introduces a Pfaffian-type variational wave function that improves upon the Gutzwiller wave function for the 1D t-J model, accurately describing its phase diagram and correlations.

Findings

GWF captures the phase structure of doped holes but fails at general J/t and n.

Residual charge correlations are described by an XXZ-type Hamiltonian.

The Pfaffian wave function reproduces the phase diagram and correlation functions.

Abstract

We find the Gutzwiller projected Fermi sea wave function(GWF) has the correct phase structure to describe the kink nature of the doped holes in the ground state of the one dimensional $t-J$ model. We find the failure of the GWF for general value of $J/t$ and electron density $n$ can be attributed to the residual charge correlation in the ground state. We find such residual charge correlation is well described by a XXZ-type effective Hamiltonian. Based on these observations, a Pfaffian-type variational wave function is proposed and is found to reproduce correctly the global phase diagram and corresponding correlation functions of the one dimensional $t-J$ model, including the Luther-Emery phase in the low electron density and large $J/t$ region.