Circuit Complexity across a Topological Phase Transition

Understand

We use Nielsen's geometric approach to quantify the circuit complexity in a one-dimensional Kitaev chain across a topological phase transition.

• We find that the circuit complexities of both the ground states and non-equilibrium steady states of the Kitaev model exhibit non-analytical behaviors at the critical points, and thus can be used to detect both {\it equilibrium} and {\it dynamical} topological phase transitions.
• Moreover, we show that the locality property of the real-space optimal Hamiltonian connecting two different ground states depends crucially on whether the two states belong to the same or different phases.
• This provides a concrete example of classifying different gapped phases using Nielsen's circuit complexity.