Separation of quadrupole, spin, and charge across the magnetic phases of a one-dimensional interacting spin-1 gas

TL;DR

This paper investigates the low-energy collective excitations of a one-dimensional spin-1 Bose gas, revealing a novel separation of quadrupole, spin, and charge sectors, and explores phase transitions using bosonization and numerical simulations.

Contribution

It introduces a new separation of quadrupole, spin, and charge sectors in a 1D spin-1 Bose gas, supported by bosonization and time-MPS simulations, and analyzes phase transitions in the system.

Findings

Identification of quadrupole-spin-charge separation.

Observation of superfluid-Mott insulator transition.

Magnetic phase diagrams for different regimes.

Abstract

We study the low-energy collective properties of a 1D spin-1 Bose gas using bosonization. After giving an overview of the technique, emphasizing the physical aspects, we apply it to the $S=1$ Bose-Hubbard Hamiltonian and find a novel separation of the quadrupole-spin-charge sectors, confirmed by time-MPS numerical simulations. Additionally, through the single particle spectrum, we show the existence of the superfluid-Mott insulator transition and the point at which the physics are described by a Heisenberg-like Hamiltonian. The magnetic phase diagrams are found for both the superfluid and insulating regimes; the latter is determined by decomposing the complete Heisenberg bilinear-biquadratic Hamiltonian, which describes the Mott insulator, into simpler, effective Hamiltonians. This allows us to keep our methods flexible and transferable to other interesting interacting condensed matter systems.