Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons

Naim E. Mackel1, Jing Yang1,2, and Adolfo del Campo1,3

1Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
2Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns vag 12, 106 91 Stockholm, Sweden
3Donostia International Physics Center, E-20018 San Sebastián, Spain

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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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Cited by

[1] Sebastian Nagies, Botao Wang, Adam C. Knapp, André Eckardt, and Nathan L. Harshman, "Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension", SciPost Physics 16 3, 086 (2024).

[2] Dimpi Thakuria, Abhay Srivastav, Brij Mohan, Asmita Kumari, and Arun Kumar Pati, "Generalised quantum speed limit for arbitrary time-continuous evolution", Journal of Physics A Mathematical General 57 2, 025302 (2024).

[3] Jing Yang and Adolfo del Campo, "Exact Quantum Dynamics, Shortcuts to Adiabaticity, and Quantum Quenches in Strongly-Correlated Many-Body Systems: The Time-Dependent Jastrow Ansatz", arXiv:2210.14937, (2022).

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