Dynamics for the Haldane phase in the Bilinear-Biquadratic Model

TL;DR

This paper investigates the dynamics of the Haldane phase in the bilinear-biquadratic model, focusing on defect minimization during quenches and the behavior of string order when transitioning between topological phases.

Contribution

It introduces optimized quench protocols to reduce defects and explores how quenching paths affect string order in topological phase transitions.

Findings

Quenches from Neel to Haldane can enhance string order beyond ground state levels.

Different quench paths significantly influence the fate of string order.

Protocols can be designed to minimize defects in the Haldane phase.

Abstract

The BBM is a promising candidate to study spin-one systems and to design quantum simulators based on its underlying Hamiltonian. The variety of different phases contains amongst other valuable and exotic phases the Haldane phase. We study the Kibble-Zurek physics of linear quenches into the Haldane phase. We outline ideal quench protocols to minimize defects in the final state while exploiting different linear quench protocols via the uniaxial or interaction term. Furthermore, we look at the fate of the string order when quenching from a topologically non-trivial phase to a trivial phase. Our studies show this depends significantly on the path chosen for quenching; for example, we discover quenches from \Neel{} to Haldane phase which reach a string order greater than their ground state counterparts for the initial or final state at intermediate quench times.