Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons

• URL: http://arxiv.org/abs/2210.10776v3
• Date: Mon, 18 Dec 2023 12:02:32 GMT
• Title: Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons
• Authors: Naim E. Mackel, Jing Yang, Adolfo del Campo
• Abstract summary: We characterize the geometry of quantum states associated with different values of $kappa$, i.e., different quantum statistics. We characterize this decay using quantum speed limits on the flow of $kappa$, illustrate our results with a model of hard-core anyons, and discuss possible experiments in quantum simulation.
• Score: 2.9491988705158843
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many-particle quantum systems with intermediate anyonic exchange statistics are supported in one spatial dimension. In this context, the anyon-anyon mapping is recast as a continuous transformation that generates shifts of the statistical parameter $\kappa$. We characterize the geometry of quantum states associated with different values of $\kappa$, i.e., different quantum statistics. While states in the bosonic and fermionic subspaces are always orthogonal, overlaps between anyonic states are generally finite and exhibit a universal form of the orthogonality catastrophe governed by a fundamental statistical factor, independent of the microscopic Hamiltonian. We characterize this decay using quantum speed limits on the flow of $\kappa$, illustrate our results with a model of hard-core anyons, and discuss possible experiments in quantum simulation.

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