Spontaneous time-reversal symmetry breaking without magnetism in a $S=1$ chain

TL;DR

This paper demonstrates the existence of a novel phase, the directional scalar spin chiral order, in a spin-1 chain, which breaks time-reversal symmetry without magnetism, using advanced DMRG analysis.

Contribution

It provides the first proof of the DSSCO phase in a spin-1 chain with complex interactions through large-scale DMRG simulations.

Findings

DSSCO exists in a spin-1 chain with specific interactions.

First order transitions from DSSCO to Haldane and spin-quadrupolar phases.

Method for detecting topological edge states in the Haldane phase.

Abstract

States of matter that break time-reversal symmetry are invariably associated with magnetism or circulating currents. Recently, one of us proposed a phase, the directional scalar spin chiral order (DSSCO), as an exception: it breaks time-reversal symmetry via chiral ordering of spins along a particular direction, but is spin-rotation symmetric. In this work, we prove the existence of this state via state-of-the-art density matrix renormalization group (DMRG) analysis on a spin-1 chain with nearest-neighbor bilinear-biquadratic interactions and additional third-neighbor ferromagnetic Heisenberg exchange. Despite the large entanglement introduced by the third-neighbor coupling, we are able to access system sizes up to $L=918$ sites. We find first order phase transitions from the DSSCO into the famous Haldane phase as well as a spin-quadrupolar phase where spin nematic correlations dominate. In the Haldane phase, we propose and demonstrate a method for detecting the topological edge states using DMRG that could be useful for other topological phases too.