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SUMMARY:Thermal entropy and entanglement transitions from modular objects 
 - Erik Tonni (SISSA)
DTSTART:20251009T090000Z
DTEND:20251009T103000Z
UID:TALK237625@talks.cam.ac.uk
DESCRIPTION:The reduced density matrix of a spatial subsystem can be writt
 en as the exponential of the modular Hamiltonian (a.k.a. entanglement Hami
 ltonian) and its eigenvalues provide the entanglement entropy. Hence\, thi
 s operator contains a lot of information about the entanglement of the cor
 responding spatial bipartition. Within Algebraic Quantum Field Theory\, th
 e modular Hamiltonian and the modular conjugation are two essential tools 
 of the &nbsp\;Tomita-Takesaki modular theory. In the first part of this ta
 lk\, it is shown how the modular conjugation in a 2D CFT at finite tempera
 ture provides the thermal entropy of a single interval of finite length. T
 he gravitational dual interpretation of this result in terms of geodesic b
 it threads is also discussed\, including its extension to higher dimension
 s for the case where the spatial subsystem is supported in a spherical reg
 ion. In the second part of the talk\, considering the harmonic chain in it
 s ground state and in large mass regime\, the entanglement Hamiltonian of 
 two disjoint blocks is explored\, showing the it displays geometric transi
 tions as the the distance between two blocks of fixed lengths vary.
LOCATION:Seminar Room 2\, Newton Institute
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