Variational state based on the Bethe ansatz solution and a correlated singlet liquid state in the one-dimensional t-J model

TL;DR

This paper introduces new variational wave functions based on the Bethe ansatz and correlated singlet states to accurately describe the ground-state phases of the one-dimensional t-J model, including Tomonaga-Luttinger and Luther-Emery liquids.

Contribution

It proposes novel variational wave functions that incorporate Bethe ansatz solutions and Jastrow factors, improving the description of different phases in the 1D t-J model.

Findings

Accurately reproduces Tomonaga-Luttinger liquid properties

Identifies Luther-Emery liquid behavior with enhanced superconducting correlations

Determines the phase diagram using the new variational states

Abstract

The one-dimensional t-J model is investigated by the variational Monte Carlo method. A variational wave function based on the Bethe ansatz solution is newly proposed, where the spin-charge separation is realized, and a long-range correlation factor of Jastrow-type is included. In most regions of the phase diagram, this wave function provides an excellent description of the ground-state properties characterized as a Tomonaga-Luttinger liquid; Both of the amplitude and exponent of correlation functions are correctly reproduced. For the spin-gap phase, another trial state of correlated singlet pairs with a Jastrow factor is introduced. This wave function shows generalized Luther-Emery liquid behavior, exhibiting enhanced superconducting correlations and exponential decay of the spin correlation function. Using these two variational wave functions, the whole phase diagram is determined. In addition, relations between the correlation exponent and variational parameters in the trial functions are derived.