Year: 2026
Type: preprint
Abstract: Shannon-R\'enyi entropies extract universal information from the full measurement distribution of a quantum many-body state and have recently become experimentally accessible probes of conformal data. Yet their microscopic evaluation remains difficult even in exactly solvable free-fermion systems. We show that the Born distribution of the critical transverse-field Ising chain is exactly the parity boundary of a weak inverse-square classical Ising model, a structure revealed by the Cauchy form of its probability kernel. The construction is exact at finite size for every real $n>0$ and isolates the long-distance sectors controlling the $n>1$ thermodynamics. Cutting a finite interval generates the universal $c\,n/[8(n-1)]$ logarithm directly from the missing $1/r^2$ interactions, with $c=1/2$ the Ising central charge. On the ring, the explicit finite-size factor has no constant term, while any additional noninteger singularity is confined to a residual cycle-only free energy. All explicit long-distance contributions become marginal only at $n=1$.
Source: arXiv (Cornell University)
Author: Rajabpour, M A
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212227499
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