Out-of-time-order correlation as a witness for topological phase transitions

We propose a physical witness for dynamically detecting topological phase transitions (TPTs) via an ex-perimentally observable out-of-time-order correlation (OTOC). The distinguishable OTOC dynamics appears in the topological trivial and nontrivial phases due to the topological locality. In the long-time limit, the OTOC undergoes a zero-to-finite-value transition at the critical point of the TPTs. This transition is robust to the choices of the initial state of the system and the operators used in the OTOC. The proposed OTOC witness can be applied to systems with and without chiral symmetry, e.g., the lattices described by the Su-Schrieffer-Heeger model, Creutz model, and Haldane model. Moreover, our proposal, as a physical witness in real space, is still valid even in the presence of disorder. Our work fundamentally brings the OTOC into the realm of TPTs and offers the prospect of exploring topological physics with quantum correlations.

Automated summary

We propose a physical witness for detecting topological phase transitions (TPTs) using an experimentally observable out-of-time-order correlation (OTOC). The OTOC dynamics can distinguish between topological trivial and nontrivial phases due to topological locality. In the long-time limit, the OTOC undergoes a zero-to-finite-value transition at the critical point of the TPTs. This proposed OTOC witness is robust and can be applied to systems with and without chiral symmetry, even in the presence of disorder.