%0 Journal Article %J Physical Review Research %D 2020 %T Circuit Complexity across a Topological Phase Transition %A Fangli Liu %A Rex Lundgren %A Paraj Titum %A James R. Garrison %A Alexey V. Gorshkov %X

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.

%B Physical Review Research %V 2 %P 013323 %8 03/16/2020 %G eng %U https://arxiv.org/abs/1902.10720 %N 1 %R https://doi.org/10.1103/PhysRevResearch.2.013323