Dynamical properties of the one-dimensional spin-1/2 Bose-Hubbard model near Mott-insulator to ferromagnetic liquid transition

TL;DR

This paper explores the dynamical behavior of the one-dimensional spin-1/2 Bose-Hubbard model near the transition from a Mott insulator to a ferromagnetic liquid, revealing a complete separation of spin and density dynamics across all energy scales.

Contribution

It demonstrates the complete separation of spin and density degrees of freedom near the transition, enabling analytical derivation of spin wave propagators and magnon peak shapes.

Findings

Complete spin-density separation at the transition

Analytical expressions for transverse spin wave propagator

Characterization of magnon peak in the dynamic spin structure factor

Abstract

We investigate the dynamics of the one-dimensional strongly repulsive spin-1/2 Bose-Hubbard model for filling $\nu\le1.$ While at $\nu=1$ the system is a Hubbard-Mott insulator exhibiting dynamical properties of the Heisenberg ferromagnet, at $\nu<1$ it is a ferromagnetic liquid with complex spin dynamics. We find that close to the insulator-liquid transition the system admits for a complete separation of spin and density degrees of freedom valid at {\it all} energy and momentum scales within the $t-J$ approximation. This allows us to derive the propagator of transverse spin waves and the shape of the magnon peak in the dynamic spin structure factor.