Entanglement asymmetry in CFT and its relation to non-topological defects
In: Journal of High Energy Physics, Jg. 2024 (2024), Heft 5, S. 1-38
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Zugriff:
Abstract The entanglement asymmetry is an information based observable that quantifies the degree of symmetry breaking in a region of an extended quantum system. We investigate this measure in the ground state of one dimensional critical systems described by a CFT. Employing the correspondence between global symmetries and defects, the analysis of the entanglement asymmetry can be formulated in terms of partition functions on Riemann surfaces with multiple non-topological defect lines inserted at their branch cuts. For large subsystems, these partition functions are determined by the scaling dimension of the defects. This leads to our first main observation: at criticality, the entanglement asymmetry acquires a subleading contribution scaling as log ℓ/ℓ for large subsystem length ℓ. Then, as an illustrative example, we consider the XY spin chain, which has a critical line described by the massless Majorana fermion theory and explicitly breaks the U(1) symmetry associated with rotations about the z-axis. In this situation the corresponding defect is marginal. Leveraging conformal invariance, we relate the scaling dimension of these defects to the ground state energy of the massless Majorana fermion on a circle with equally-spaced point defects. We exploit this mapping to derive our second main result: the exact expression for the scaling dimension associated with n defects of arbitrary strengths. Our result generalizes a known formula for the n = 1 case derived in several previous works. We then use this exact scaling dimension to derive our third main result: the exact prefactor of the log ℓ/ℓ term in the asymmetry of the critical XY chain.
Titel: |
Entanglement asymmetry in CFT and its relation to non-topological defects
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Autor/in / Beteiligte Person: | Fossati, Michele ; Ares, Filiberto ; Dubail, Jérôme ; Calabrese, Pasquale |
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Zeitschrift: | Journal of High Energy Physics, Jg. 2024 (2024), Heft 5, S. 1-38 |
Veröffentlichung: | SpringerOpen, 2024 |
Medientyp: | academicJournal |
ISSN: | 1029-8479 (print) |
DOI: | 10.1007/JHEP05(2024)059 |
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