Symmetry & Controllability for Spin Networks with a Single-Node Control

Understand

We consider the relation of symmetries and subspace controllability for spin networks with XXZ coupling subject to control of a single node by a local potential (Z-control).

• Such networks decompose into excitation subspaces.
• Focusing on the single excitation subspace it is shown that for single-node Z-controls external symmetries are characterized by eigenstates of the system Hamiltonian that have zero overlap with the control node, and there are no internal symmetries.
• It is further shown that there are symmetries that persist even in the presence of random perturbations.