Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons

TL;DR

This paper explores the geometry and orthogonality properties of one-dimensional anyonic quantum states, revealing a universal orthogonality catastrophe governed by statistical factors, with implications for quantum simulation.

Contribution

It introduces a continuous transformation framework for anyonic states, characterizes their geometric properties, and uncovers a universal orthogonality catastrophe independent of microscopic details.

Findings

States with different statistics have finite overlaps with a universal decay form.

Orthogonality catastrophe is governed by a fundamental statistical factor.

Quantum speed limits relate to the flow of the statistical parameter .

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.