Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>κ</mml:mi></mml:math>. We characterize the geometry of quantum states associated with different values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>κ</mml:mi></mml:math>, 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>κ</mml:mi></mml:math>, illustrate our results with a model of hard-core anyons, and discuss possible experiments in quantum simulation.