Abstract
In the presence of a global symmetry, the entanglement entropy of a quantum system can be decomposed among the individual symmetry sectors, dubbed symmetry-resolved entanglement entropy. For a conformal field theory with Abelian symmetry, it obeys the equipartition theorem in the scaling limit, i.e., at the leading order, the entanglement is distributed equally between different symmetry sectors. In this work, we examine the thermal corrections to a single interval symmetry-resolved Rényi and entanglement entropies for two-dimensional conformal field theories on a circle. Using a low-temperature expansion of the thermal density matrix, we find that in addition to the mass gap and the degeneracy of the first excited state, these universal corrections depend also on the four-point correlation function of the primary fields. We also obtain thermal corrections to the full counting statistics of the ground state and define the probability fluctuations function which scales as \( {e}^{-2\pi {\Delta}_{\psi}\beta /L} \), where ∆ψ is the scaling dimension of the lowest weight states. As an example, we explicitly evaluate the thermal corrections to the symmetry-resolved entanglement entropy and FCS for the spinless fermions and find a term breaking entanglement equipartition at order (log l)−2.
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Acknowledgments
Thanks to Pasquale Calabrese, Luca Capizzi, Ghadir Jafari, Mojtaba Mohammadi Najafabadi, Sepideh Mohammadi, Sara Murciano, Ali Naseh, Reza Pirmoradian, Hesam Soltanpanahi, Behrad Taghavi, and Hamed Zolfi for helpful discussions on our manuscript. We are also grateful to JHEP referee who made several very helpful suggestions that improved our manuscript.
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Ghasemi, M. Universal thermal corrections to symmetry-resolved entanglement entropy and full counting statistics. J. High Energ. Phys. 2023, 209 (2023). https://doi.org/10.1007/JHEP05(2023)209
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DOI: https://doi.org/10.1007/JHEP05(2023)209