Abstract
Global symmetries of quantum many-body systems can be spontaneously broken. Whenever this mechanism happens, the ground state is degenerate and one encounters an ordered phase. In this study, our objective is to investigate this phenomenon by examining the entanglement asymmetry of a specific region. This quantity, which has recently been introduced in the context of U(1) symmetry breaking, is extended to encompass arbitrary finite groups G. We also establish a field theoretic framework in the replica theory using twist operators. We explicitly demonstrate our construction in the ordered phase of the Ising field theory in 1+1 dimensions, where a ℤ2 symmetry is spontaneously broken, and we employ a form factor bootstrap approach to characterise a family of composite twist fields. Analytical predictions are provided for the entanglement asymmetry of an interval in the Ising model as the length of the interval becomes large. We also propose a general conjecture relating the entanglement asymmetry and the number of degenerate vacua, expected to be valid for a large class of states, and we prove it explicitly in some cases.
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Acknowledgments
The authors are grateful to Pasquale Calabrese, David Horvath, Alessandro Santini, Guido Giachetti, Olalla Castro Alvaredo and Filiberto Ares for the useful discussions. Michele Mazzoni is grateful for funding under the EPSRC Mathematical Sciences Doctoral Training Partnership EP/W524104/1 and wants to thank SISSA for hospitality during a one-month visit in which most of this work was completed. LC acknowledges support from ERC under Consolidator grant number 771536 (NEMO).
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Capizzi, L., Mazzoni, M. Entanglement asymmetry in the ordered phase of many-body systems: the Ising field theory. J. High Energ. Phys. 2023, 144 (2023). https://doi.org/10.1007/JHEP12(2023)144
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DOI: https://doi.org/10.1007/JHEP12(2023)144