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arXiv:2511.01366 · Journal of High Energy Physics

Symmetry-resolved entanglement entropy from heat kernels

Yuan-Chun Jing, Chao Niu, Zhuo-Yu Xian

Published May 5, 2026• 0 citations

Abstract

A bstract We develop a systematic framework for computing symmetry-resolved entanglement entropies (SREE) in charged quantum systems based on an improved heat kernel approach. Although the conventional Sommerfeld formula proves effective for neutral systems, it encounters limitations when gauge fields or chemical potentials are introduced due to incomplete residue prescriptions and violations of asymptotic boundary conditions. By reconstructing the analytic structure of the heat kernel using a phase factor, we derive a globally convergent expansion that reconciles discrete residue summations with continuous spectral decompositions. We further apply this framework to Gaussian continuous multi-scale entanglement renormalization ansatz (cMERA) states and show that the entanglement entropy (EE) can be expressed in terms of the cMERA flow functions. In particular, we obtain a symmetry-resolved entanglement entropy flow equation in the presence of a chemical potential. This formulation extends naturally to arbitrary spacetime dimensions and recovers established results for neutral systems in the μ → 0 limit. We validate our framework through two settings: (1) exact agreement with (1 + 1)-dimensional conformal field theory (CFT) predictions using twist-operator techniques, and (2) consistency with holographic entropy calculations on S 1 × H d −1 geometries. Our results both unify the treatment of charged and neutral entanglement entropy and extend this treatment to real-space renormalization frameworks, providing a robust tool for probing symmetry-resolved entanglement in conformal field theories, their holographic duals, and cMERA representations.

DOI: 10.1007/jhep05(2026)039

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Rényi entropies, S_{n}, admit a natural generalization in the presence of global symmetries. These "charged Rényi entropies" are functions of the chemical potential μ conjugate to the charge contained in the entangling region and reduce to the usual notions as μ→0. For n=1, this provides a notion of charged entanglement entropy. In this Letter, we prove that for a general d(≥3)-dimensional conformal field theory, the leading correction to the uncharged entanglement entropy across a spherical entangling surface is quadratic in the chemical potential, positive definite, and universally controlled (up to fixed d-dependent constants) by the coefficients C_{J} and a_{2}. These fully characterize, for a given theory, the current correlators ⟨JJ⟩ and ⟨TJJ⟩, as well as the energy flux measured at infinity produced by the insertion of the current operator. Our result is motivated by analytic holographic calculations for a special class of higher-curvature gravities coupled to a (d-2) form in general dimensions as well as for free fields in d=4. A proof for general theories and dimensions follows from previously known universal identities involving the magnetic response of twist operators introduced in A. Belin et al. [J. High Energy Phys. 12 (2013) 059.JHEPFG1029-847910.1007/JHEP12(2013)059] and basic thermodynamic relations.

Abstract We develop a general approach to compute the symmetry-resolved Rényi and von Neumann entanglement entropies (SREE) of thermodynamic macrostates in interacting integrable systems. Our method is based on a combination of the thermodynamic Bethe ansatz and the Gärtner–Ellis theorem from large deviation theory. We derive an explicit simple formula for the von Neumann SREE, which we show to coincide with the thermodynamic Yang–Yang entropy of an effective macrostate determined by the charge sector. Focusing on the XXZ Heisenberg spin chain, we test our result against iTEBD calculations for thermal states, finding good agreement. As an application, we provide analytic predictions for the asymptotic value of the SREE following a quantum quench.