# Magnetic phase transitions of insulating spin-orbit coupled Bose atoms in one-dimensional optical lattices

## TL;DR

This paper investigates magnetic phase transitions in insulating spin-orbit coupled Bose atoms in one-dimensional optical lattices, revealing how interactions and external fields influence magnetic order and quantum phases.

## Contribution

It introduces a detailed analysis of magnetic phases using matrix product states, highlighting the effects of spin-orbit coupling, interactions, and transverse fields on quantum magnetism.

## Key findings

- Gapped ferromagnetic phase with long-range order when no transverse field.
- Gapless Luttinger liquid phase with algebraic correlations under certain interactions.
- Emergence of long-range ordered phases with transverse field and Dzyaloshinskii-Moriya interaction.

## Abstract

We consider the insulating spin-orbit coupled Bose atoms confined within one-dimensional optical lattices and explore their ground-state magnetic phase transitions. Under strong interactions, the charge degrees of atoms are frozen and the system can be described by an anisotropic XXZ Heisenberg chain with Dzyaloshinskii-Moriya interaction and transverse field. We apply the matrix product state method to obtain low-energy states and analyze the lowest energy gaps and the ground-state magnetization and correlations. We find when the transverse field is absent, the ground state is a gapped ferromagnetic phase with long-range correlation in the z direction if the interspin s-wave interacting strength is stronger than that of the intraspin one, otherwise it is a gapless Luttinger liquid (LL) phase with algebraic decaying correlation. When the transverse field is turned on, the gapless LL phase is broken, there emerges a long-range correlated phase with ferromagnetic, antiferromagnetic or spiral order, which depends on the DM interaction strength. We believe our study provides a complete understanding of the interplay between SOC and quantum magnetism of spinor atoms in optical lattices.