



01525nas a2200181   4500008004100000245006100041210006100102260001500163300001100178490000600189520101100195100001601206700001801222700001701240700002401257700002501281856003701306       2020                        eng d00aCircuit Complexity across a Topological Phase Transition0 aCircuit Complexity across a Topological Phase Transition  c03/16/2020  a0133230 v23 a<p>We use Nielsen&#39;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.</p>1 aLiu, Fangli1 aLundgren, Rex1 aTitum, Paraj1 aGarrison, James, R.1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/1902.10720