Circuit Complexity across a Topological Phase Transition

TitleCircuit Complexity across a Topological Phase Transition
Publication TypeJournal Article
Year of Publication2020
AuthorsLiu, F, Lundgren, R, Titum, P, Garrison, JR, Gorshkov, AV
JournalPhysical Review Research
Date Published03/16/2020

We use Nielsen's approach to quantify the circuit complexity in the one-dimensional Kitaev model. In equilibrium, we find that the circuit complexity of ground states exhibits a divergent derivative at the critical point, signaling the presence of a topological phase transition. Out of equilibrium, we study the complexity dynamics after a sudden quench, and find that the steady-state complexity exhibits nonanalytical behavior when quenched across critical points. We generalize our results to the long-range interacting case, and demonstrate that the circuit complexity correctly predicts the critical point between regions with different semi-integer topological numbers. Our results establish a connection between circuit complexity and quantum phase transitions both in and out of equilibrium, and can be easily generalized to topological phase transitions in higher dimensions. Our study opens a new avenue to using circuit complexity as a novel quantity to understand many-body systems.