Winding up quantum spin helices: How avoided level crossings exile classical topological protection

TL;DR

This paper investigates how quantum effects, such as avoided level crossings, disrupt classical topological protection in quantum Heisenberg chains, but certain anisotropies and dynamical methods can restore stable spin helices and enable qubit formation.

Contribution

It reveals the breakdown of classical topological protection in quantum chains due to avoided level crossings and identifies conditions under which stable, entangled spin helices and qubits can be realized.

Findings

Avoided level crossings cause spin slippage in finite quantum chains.

Stable spin helices re-emerge at specific anisotropy values.

Half-integer odd-length chains host qubits with non-trivial Berry phases.

Abstract

A magnetic helix can be wound into a classical Heisenberg chain by fixing one end while rotating the other one. We show that in quantum Heisenberg chains \new{of finite length}, the magnetization slips back to the trivial state beyond a finite turning angle. Avoided level crossings thus undermine classical topological protection. Yet, for special values of the axial Heisenberg anisotropy, stable spin helices form again, which are non-locally entangled. Away from these sweet spots, spin helices can be stabilized dynamically or by dissipation. For half-integer spin chains of odd length, a spin slippage state and its Kramers partner define a qubit with a non-trivial Berry connection.