# Directional current-current correlation functions in a two-species hard-core bosons in one dimensional finite lattice: An exact diagonalization study

## TL;DR

This study investigates a two-species hard-core boson model in one dimension, revealing phase transitions and current correlations through exact diagonalization, with implications for understanding superfluid, Mott insulator, and charge-density-wave phases.

## Contribution

It provides an exact diagonalization analysis of current correlations in a two-species bosonic model, highlighting finite-size effects and phase transition behaviors.

## Key findings

- Counter-flow persists in the Mott insulator region for finite lattices.
- Co-flow occurs in the charge-density-wave region.
- Phase transition from superfluid to Mott insulator explained by one-band theory.

## Abstract

We study a model for two-species hard-core bosons in one dimension. In this model, the same-species bosons have a hard-core condition at the same site, while different-species bosons are allowed to occupy the same site with a local interaction $U$. At half-filling, by Jordan-Wigner transformation, the model can be exactly mapped to a fermionic Hubbard model. Due to this correspondence, the phase transition from superfluid ($U=0$) to Mott insulator ($U>0$) can be explained by simple one-band theory at half-filling. By using an exact diagonalization method adopting a modified Lanczos method, we obtain the ground states as a function of $U$ for the lattice size upto $L=16$. We calculate directional current-current correlation functions in this model, which indicate that there are some remaining counter-flow in the Mott insulating region ($U>0$) and co-flow in the charge-density-wave region ($U<0$) for the finite lattices.