# Magnetic phases of spin-1 lattice gases with random interactions

## TL;DR

This paper investigates how random spin-dependent interactions in a spin-1 lattice gas lead to complex magnetic phases, including disordered ferromagnetic and dimer phases, using advanced numerical methods.

## Contribution

It introduces a detailed analysis of disordered magnetic phases in spin-1 lattice gases with local ferromagnetic or antiferromagnetic interactions, revealing new disordered phases.

## Key findings

- Disordered ferromagnetic phase with spin-glass order parameter
- Absence of random singlet order in certain regions
- Identification of phase boundaries between ferromagnetic and dimer phases

## Abstract

A spin-1 atomic gas in an optical lattice, in the unit-filling Mott Insulator (MI) phase and in the presence of disordered spin-dependent interaction, is considered. In this regime, at zero temperature, the system is well described by a disordered rotationally-invariant spin-1 bilinear-biquadratic model. We study, via the density matrix renormalization group algorithm, a bounded disorder model such that the spin interactions can be locally either ferromagnetic or antiferromagnetic. Random interactions induce the appearance of a disordered ferromagnetic phase characterized by a non-vanishing value of spin-glass order parameter across the boundary between a ferromagnetic phase and a dimer phase exhibiting random singlet order. The study of the distribution of the block entanglement entropy reveals that in this region there is no random singlet order.