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This study demonstrates that finite-temperature stabilizer entropy in critical quantum spin chains can be exactly reduced to a single Pfaffian, revealing hidden conformal data that standard thermodynamic probes miss. By identifying a level-eight eta quotient as the universal scaling function, the work provides a precise mathematical framework for analyzing high-temperature crossovers in the transverse-field Ising model. These findings offer a refined tool for extracting defect-like information from quantum many-body systems, bridging gaps between statistical mechanics and conformal field theory.
Hidden Conformal Boundary Data in Finite-Temperature Stabilizer Entropy
arXiv:2606.08606v1 Announce Type: new Abstract: We study the finite-temperature stabilizer R\'enyi entropy of the open critical quantum spin chains. At R\'enyi index one half, this observable probes the distribution of thermal Pauli-string expectation values and can be written as a sum over absolute values of all square minors of a finite-temperature correlation matrix for the transverse-field Ising chain. We show that this exponentially large sum is exactly reducible to a single Pfaffian. The Pfaffian representation reveals a block Toeplitz--Hankel structure and allows us to extract the large-size scaling in several thermal regimes. In the crossover window where the inverse temperature is proportional to the system size, the stabilizer entropy factorizes into a saturated extensive contribution and a universal finite-size scaling function. We find that this scaling function is a level-eight eta quotient, rather than the ordinary free-boundary Majorana thermal factor. The deviation is exponentially hidden at low temperature but controls the high-temperature crossover, where it gives a Cardy-like asymptotic for the Pauli-string expectation-weight spectrum. These results show that finite-temperature stabilizer entropy reveals hidden defect-like conformal data invisible to ordinary thermodynamic probes.
Abstract:We study the finite-temperature stabilizer Rényi entropy of the open critical quantum spin chains. At Rényi index one half, this observable probes the distribution of thermal Pauli-string expectation values and can be written as a sum over absolute values of all square minors of a finite-temperature correlation matrix for the transverse-field Ising chain. We show that this exponentially large sum is exactly reducible to a single Pfaffian. The Pfaffian representation reveals a block Toeplitz--Hankel structure and allows us to extract the large-size scaling in several thermal regimes. In the crossover window where the inverse temperature is proportional to the system size, the stabilizer entropy factorizes into a saturated extensive contribution and a universal finite-size scaling function. We find that this scaling function is a level-eight eta quotient, rather than the ordinary free-boundary Majorana thermal factor. The deviation is exponentially hidden at low temperature but controls the high-temperature crossover, where it gives a Cardy-like asymptotic for the Pauli-string expectation-weight spectrum. These results show that finite-temperature stabilizer entropy reveals hidden defect-like conformal data invisible to ordinary thermodynamic probes.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)
arXiv:2606.08606 [quant-ph]
(or arXiv:2606.08606v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.08606 arXiv-issued DOI via DataCite (pending registration)
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