Dynamics of entanglement from CFT to AdS
Dynamics of entanglement from CFT to AdS Paweł Caputa
It from Qubit, NY 07/12/2016
Outline •
Introduction/Motivation
•
Question/Challenges
•
Lessons
•
Open problems
Based on:
•
in progress with T.Takayanagi, K.Watanabe, Y.Kusuki
•
OTOs in RCFTs with T.Numasawa and A.Veliz-Osorio
•
Numerics vs CFT with M.Rams
•
Large c CFTs with T.Takayanagi and M.Nozaki
Invitation to the program!
QI
M-B
AdS
CFT
c |A| SA = log + c˜n 3 a
Motivation:
Can we be less universal and keep the “overlap” ? Small steps…
Excited states (interactions, dynamics) !
Question in 1+1 d
o
h
l ⇢(t) = e
iHt
A
O(x) |0i h0| O† (x)eiHt
SA (t) ?
How does this change the entanglement between A and its complement?
Challenges: M-B (Numerics): free fermions, MPS, (c)MERA(t)?
CFT: Lorentzian correlators, modular data (S,T, STTS…)
hO(z1 , z¯1 )...O(zn , z¯n )i = F (z, z¯)
Independent variables
Z(⌧, ⌧¯) AdS: Time dependent backgrounds (back reaction), HRT, 1/c ?
Lessons (for QI measures, OTO, relative Renyi etc.) 1) In RCFT answers can be expressed in therms of the modular S or T matrices (also time scales etc.) 2) RCFT vs non-RCFT (growth of the measures, late time behaviour) 3) There are features that depend on the central charge (large or small), that also apply to holography 4) There are features that are sensitive to the spectrum and not all measures are able to distinguish them (entropies, MI, OTO) 5) Good to borrow tools and understand them from CFT to AdS
Open Problems: Lattice operators and operators in CFT? Efficient time evolution beyond free fermions? Modular data at large c? “Lorentzian” singularities and large c, spectrum and limits of the partition functions
Lessons for and from holography? Meaning of the time scales? Very late times and holography? Poincare recurrences ?
Thank you!
It from Qubit, NY 07/12/2016
Outline •
Introduction/Motivation
•
Question/Challenges
•
Lessons
•
Open problems
Based on:
•
in progress with T.Takayanagi, K.Watanabe, Y.Kusuki
•
OTOs in RCFTs with T.Numasawa and A.Veliz-Osorio
•
Numerics vs CFT with M.Rams
•
Large c CFTs with T.Takayanagi and M.Nozaki
Invitation to the program!
QI
M-B
AdS
CFT
c |A| SA = log + c˜n 3 a
Motivation:
Can we be less universal and keep the “overlap” ? Small steps…
Excited states (interactions, dynamics) !
Question in 1+1 d
o
h
l ⇢(t) = e
iHt
A
O(x) |0i h0| O† (x)eiHt
SA (t) ?
How does this change the entanglement between A and its complement?
Challenges: M-B (Numerics): free fermions, MPS, (c)MERA(t)?
CFT: Lorentzian correlators, modular data (S,T, STTS…)
hO(z1 , z¯1 )...O(zn , z¯n )i = F (z, z¯)
Independent variables
Z(⌧, ⌧¯) AdS: Time dependent backgrounds (back reaction), HRT, 1/c ?
Lessons (for QI measures, OTO, relative Renyi etc.) 1) In RCFT answers can be expressed in therms of the modular S or T matrices (also time scales etc.) 2) RCFT vs non-RCFT (growth of the measures, late time behaviour) 3) There are features that depend on the central charge (large or small), that also apply to holography 4) There are features that are sensitive to the spectrum and not all measures are able to distinguish them (entropies, MI, OTO) 5) Good to borrow tools and understand them from CFT to AdS
Open Problems: Lattice operators and operators in CFT? Efficient time evolution beyond free fermions? Modular data at large c? “Lorentzian” singularities and large c, spectrum and limits of the partition functions
Lessons for and from holography? Meaning of the time scales? Very late times and holography? Poincare recurrences ?
Thank you!
