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arXiv · 1902.10720

Circuit Complexity across a Topological Phase Transition

Fangli Liu·Seth Whitsitt·Jonathan B. Curtis·Rex Lundgren·Paraj Titum·Zhi-Cheng Yang·James R. Garrison·Alexey V. Gorshkov
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Abstract

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. We further generalize our results to a Kitaev chain with long-range pairing, and discuss generalizations to higher dimensions. Our result opens up a new avenue for using circuit complexity as a novel tool to understand quantum many-body systems.

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Fangli Liu, Seth Whitsitt, Jonathan B. Curtis, Rex Lundgren, Paraj Titum, Zhi-Cheng Yang, James R. Garrison, Alexey V. Gorshkov. 2019-02-27. Circuit Complexity across a Topological Phase Transition. https://doi.org/10.1103/physrevresearch.2.013323

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