Hidden Conformal Boundary Data in Finite-Temperature Stabilizer Entropy

• URL: http://arxiv.org/abs/2606.08606v1
• Date: Sun, 07 Jun 2026 12:39:11 GMT
• Title: Hidden Conformal Boundary Data in Finite-Temperature Stabilizer Entropy
• Abstract summary: We study the finite-temperature stabilizer Rényi entropy of the open critical quantum spin chains.<n>We show that this exponentially large sum is exactly reducible to a single Pfaffian.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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