Speaker
Description
Characterizing a quantum system through the lens of quantum resources provides a way of understanding many-body states in terms of operational structures that are not directly captured by local observables. While quantum entanglement serves as a paradigmatic example with well-established field-theoretical foundations, recent studies have shown that quantum magic, a resource for universal quantum computation, offers distinct insights into many-body physics. In spin systems, the universal behavior of nonstabilizerness has been systematically revealed by formulating the stabilizer Rényi entropy using conformal field theory (CFT) [1]. In bosonic and fermionic systems, however, a comparable formulation for their computational resource, namely, non-Gaussianity, has been lacking due to the distinct definitions of free states.
In this work, we introduce a unified measure, the magic Rényi entropy (MRE), to quantify computational resources in spins, bosons, and fermions, and we reveal the common universal behavior of nonstabilizerness and non-Gaussianity in critical many-body states. Specifically, we show that the universal contribution to the MRE of a critical state described by a (1+1)-dimensional CFT is determined by the Affleck-Ludwig boundary entropy [2] of the corresponding infrared boundary state. Furthermore, we elucidate how non-Gaussianity can renormalize this universal contribution or drive a boundary phase transition to a distinct infrared fixed point through the bulk-boundary operator product expansion. As a concrete demonstration, we present a detailed analysis of interacting spinless fermions described by the Tomonaga-Luttinger liquid, where we derive a perturbative correction to the universal contribution and analytically show a boundary phase transition at the Luttinger parameter $K=3$. These analytical predictions are confirmed by numerical calculations with high accuracy. Our results provide a unified field-theoretical formulation for investigating the universal signatures of many-body magic across spins, bosons, and fermions.
[1] M. Hoshino, M. Oshikawa and Y. Ashida, Phys. Rev. X 16, 011037 (2026).
[2] I. Affleck and A. W. W. Ludwig, Phys. Rev. Lett. 67, 161 (1991).