# Asymptotic behavior of correlation functions of one-dimensional polar-molecules on optical lattices

## TL;DR

This paper develops an approximate theoretical framework combining slave-spin and mean-field methods to analyze correlation functions of fermionic polar molecules in one-dimensional optical lattices, highlighting the role of long-range interactions.

## Contribution

It introduces a novel combined slave-spin and mean-field approach to study correlation functions in a 1D generalized $t-J$ model with long-range interactions.

## Key findings

- Pairing correlations are linked to spin and density correlations.
- Long-range interactions influence the behavior of correlation functions.
- The method provides insights into long-range correlated fermions in 1D.

## Abstract

We combine a slave-spin approach with a mean-field theory to develop an approximate theoretical scheme to study the density, spin, and, pairing correlation functions of fermionic polar molecules. We model the polar molecules subjected to a one-dimensional periodic optical lattice potential using a generalized $t-J$ model, where the long-range part of the interaction is included through the exchange interaction parameter. For this model, we derive a set of self-consistent equations for the correlation functions, and evaluate them numerically for the long-distance behaviour. We find that the pairing correlations are related to spin correlations through the density and the slave-spin correlations. Further, our calculations indicates that the long-range character of the interaction can be probed through these correlation functions. In the absence of exact solutions for the one-dimensional $t-J$ model, our approximate theoretical treatment can be treated as a useful tool to study one dimensional long-range correlated fermions.