Abstract

Stabilizer R?nyi entropies provide a sensitive probe of how many-body quantum states are organized in Pauli space. In this talk, I will present exact results for critical, massive, and finite-temperature quantum spin chains. A central result is an exact correspondence between stabilizer R?nyi entropies of Gaussian states and Shannon?R?nyi entropies of doubled number-conserving systems. This identifies the critical transverse-field Ising chain as a common building block for several entropy quantities and gives access to universal finite-size constants, boundary logarithms, and conformal data. Away from criticality, I will show how the correlation length controls universal crossover functions for complete systems and subsystems. At finite temperature, the universal contribution is described by an eta quotient. Its modular transformation produces a Cardy-like thermal scaling law and reveals boundary- or defect-like information hidden in the Pauli spectrum but absent from ordinary thermodynamics. I will conclude with recent progress on the algebraic structure and exact solvability of the underlying all-minors partition function.