Classical Root Systems Reveal Defect-Junction Data in Stabilizer Rényi Entropy
Abstract
Universal information extracted from a critical quantum state depends on how the state is probed. Spatial entanglement, participation statistics, and stabilizer Rényi entropy correspond to different replica geometries and need not isolate the same boundary data. We show that the complete distribution of Pauli magnitudes in critical Ising chains carries an exact geometric fingerprint of boundary termination, distinguishing lattice realizations that flow to the same infrared boundary fixed point. This structure is organized by discrete Selberg ensembles associated with the classical root systems A, B, C, and D: three open chains sharing the free-free Ising boundary condition retain distinct BL, CL, and DL trigonometric wall geometries. The standard symmetry-breaking representatives instead produce rectangular, pinned, and character-inserted C ensembles. Their four boundary moments contain exactly two independent multiplicative combinations invariant under local endpoint normalizations. One of these reduces exactly at finite rank to a moment of the fundamental symplectic character and provides a lattice target for a defect-measurement-boundary junction amplitude. A conditional Gaussian-character law predicts its values throughout the unlocked phase, while exact-arithmetic finite-rank results at the α = 4 transition depart sharply from the Gaussian continuation. These results show that the full Pauli spectrum resolves boundary information invisible to the infrared boundary fixed point alone and provide concrete targets for replicated boundary conformal field theory.
Related
- Rényi Multi-entropy for Stabilizer States: A Finite Field Gauss Sum Problem
- Fast and exact approach for stabilizer Rényi entropy via the XOR-FWHT algorithm
- Spectral geometry of nonlocal stabilizer entropy
- Efficient Pauli Truncation from Operator Stabilizer Rényi Entropy
- Stabilizer Rényi Entropy Without a Phase Reference
BibTeX
@misc{rajabpour2026classical,
title = {{Classical Root Systems Reveal Defect-Junction Data in Stabilizer Rényi Entropy}},
author = {M A Rajabpour},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27537},
eprint = {2609.27537},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05760272v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classical Root Systems Reveal Defect-Junction Data in Stabilizer Rényi Entropy
AU - M A Rajabpour
PY - 2026
DA - 2026/09/23
PB - HAL
DO - 10.48550/arxiv.2609.27537
UR - https://hal.science/hal-05760272v1
AB - Universal information extracted from a critical quantum state depends on how the state is probed. Spatial entanglement, participation statistics, and stabilizer Rényi entropy correspond to different replica geometries and need not isolate the same boundary data. We show that the complete distribution of Pauli magnitudes in critical Ising chains carries an exact geometric fingerprint of boundary termination, distinguishing lattice realizations that flow to the same infrared boundary fixed point. This structure is organized by discrete Selberg ensembles associated with the classical root systems A, B, C, and D: three open chains sharing the free-free Ising boundary condition retain distinct BL, CL, and DL trigonometric wall geometries. The standard symmetry-breaking representatives instead produce rectangular, pinned, and character-inserted C ensembles. Their four boundary moments contain exactly two independent multiplicative combinations invariant under local endpoint normalizations. One of these reduces exactly at finite rank to a moment of the fundamental symplectic character and provides a lattice target for a defect-measurement-boundary junction amplitude. A conditional Gaussian-character law predicts its values throughout the unlocked phase, while exact-arithmetic finite-rank results at the α = 4 transition depart sharply from the Gaussian continuation. These results show that the full Pauli spectrum resolves boundary information invisible to the infrared boundary fixed point alone and provide concrete targets for replicated boundary conformal field theory.
ER -