# Emergent Haldane phase in the $S=1$ bilinear-biquadratic Heisenberg model on the square lattice

## TL;DR

This study uses advanced tensor network simulations to discover an unexpected Haldane phase in a 2D spin model, challenging prior assumptions of direct magnetic transitions.

## Contribution

It reveals an emergent Haldane phase in the square lattice $S=1$ bilinear-biquadratic Heisenberg model, showing a new intermediate phase not previously identified.

## Key findings

- Discovery of an emergent Haldane phase between magnetic orders
- The phase preserves SU(2) and translational symmetry
- Contradicts earlier studies suggesting direct transitions

## Abstract

Infinite projected entangled pair states simulations of the $S=1$ bilinear-biquadratic Heisenberg model on the square lattice reveal an emergent Haldane phase in between the previously predicted antiferromagnetic and 3-sublattice 120$^\circ$ magnetically ordered phases. This intermediate phase preserves SU(2) spin and translational symmetry but breaks lattice rotational symmetry, and it can be adiabatically connected to the Haldane phase of decoupled $S=1$ chains. Our results contradict previous studies which found a direct transition between the two magnetically ordered states.