On Complexity and Duality

• URL: http://arxiv.org/abs/2411.02546v1
• Date: Mon, 04 Nov 2024 19:27:21 GMT
• Title: On Complexity and Duality
• Authors: Jeff Murugan, Zayd Pandit, Hendrik J. R. van Zyl,
• Abstract summary: We find that non-local operators exhibit behavior that mimics the growth of their local counterparts. Our results shed light on the intricate relationship between non-locality, complexity growth, and duality in quantum systems.
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• Abstract: We explore the relationship between complexity and duality in quantum systems, focusing on how local and non-local operators evolve under time evolution. We find that non-local operators, which are dual to local operators under specific mappings, exhibit behavior that mimics the growth of their local counterparts, particularly when considering state complexity. For the open transverse Ising model this leads to a neat organisation of the operator dynamics on either side of the duality, both consistent with growth expected in a quadratic fermion model like the Kitaev chain. When examing periodic chains, however, the mapping of boundary terms provides access to multiple branches of highly complex operators. These give rise to much larger saturation values of complexity for parity-mixing operators and are in contrast to what one would expect for a quadratic Hamiltonian. Our results shed light on the intricate relationship between non-locality, complexity growth, and duality in quantum systems.

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