Infinite coherence time of edge spins in finite-length chains

Abstract

Motivated by the recent observation that exponentially long coherence times can be achieved for edge spins in models with strong zero modes, we study the impact of level crossings in finite-length spin chains on the dynamics of the edge spins. Focussing on the XY spin-1=2 chain with transverse or longitudinal magnetic field, two models relevant to understand recent experimental results on cobalt adatoms, we show that the edge spins can remain coherent for an infinite time even for a finite-length chain if the magnetic field is tuned to a value at which there is a level crossing. Furthermore, we show that the edge spins remain coherent for any initial state for the integrable case of transverse field because all states have level crossings at the same value of the field, while the coherence time is increasingly large for lower temperatures in the case of longitudinal field, which is non-integrable.

arXiv comment7 pages, 6 figures

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• Decoherence and relaxation of topological states in extended quantum Ising models
• Almost Strong Zero Modes at Finite Temperature
• Even and odd normalized zero modes in random interacting Majorana models respecting the Parity $P$ and the Time-Reversal-Symmetry $T$
• Allosteric impurity effects in long spin chains
• Construction of Many-Body-Localized Models where all the eigenstates are Matrix-Product-States
• Observability of a Sharp Majorana Transition in a Few-Body Model
• Perturbative approach to quantum tunneling and quantum interferences in spin clusters