Quantum chaos, thermodynamics and black hole microstates in the mass deformed SYK model
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Springer
Received: January Revised: May Accepted: July Published: August
18, 28, 16, 19,
2020 2020 2020 2020
Tomoki Nosakaa,b and Tokiro Numasawac a
INFN Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy b International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy c Department of Physics, McGill University, 3600 Rue University, Montreal, Quebec H3A 2T8, Canada
E-mail: [email protected], [email protected] Abstract: We study various aspects of the mass deformation of the SYK model which makes the black hole microstates escapable. SYK boundary states are given by a simple local boundary condition on the Majorana fermions and then evolved in Euclidean time in the SYK Hamiltonian. We study the ground state of this mass deformed SYK model in detail. We also use SYK boundary states as a variational approximation to the ground state of the mass deformed SYK model. We compare variational approximation with the exact ground state results and they showed a good agreement. We also study the time evolution of the mass deformed ground state under the SYK Hamiltonian. We give a gravity interpretation of the mass deformed ground state and its time evolutions. In gravity side, mass deformation gives a way to prepare black hole microstates that are similar to pure boundary state black holes. Escaping protocol on these ground states simply gives a global AdS2 with an IR end of the world brane. We also study the thermodynamics and quantum chaotic properties of this mass deformed SYK model. Interestingly, we do not observe the Hawking Page like phase transition in this model in spite of similarity of the Hamiltonian with eternal traversable wormhole model where we have the phase transition. Keywords: AdS-CFT Correspondence, Black Holes in String Theory, Holography and condensed matter physics (AdS/CMT), Random Systems ArXiv ePrint: 1912.12302
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP08(2020)081
JHEP08(2020)081
Quantum chaos, thermodynamics and black hole microstates in the mass deformed SYK model
Contents 1 Introduction and summary 1.1 Summary of the paper
1 3 5 5 6 8 9 11 12
3 Large N , finite q analysis 3.1 Solving the model in the conformal limit 3.2 Variational approximation for the ground state 3.2.1 Variational approximation in conformal limit 3.2.2 Comparison of variational approximation and exact ground state 3.3 Thermodynamics of the deformed SYK model
14 16 20 20 22 23
4 Finite N analysis of the model 4.1 Overlap β hB(↓,↓,··· ,↓) |0(+) i 4.2 Chaotic property
25 25 29
5 Large N , large q analysis 5.1 Large q limit at zero temperature 5.2 Variational approximation in the large q limit 5.3 Large q limit at finite temperature 5.3.1 Inverse temperature of order β = q log q 5.3.2 Inverse temperature of order β = q √ 5.3.3 Inverse temperature of order β = q 5.3.4 Temperature of order β = 1 5.4 Computing the overlap at large q limit
31 32 34 35 36 37 38 39 40
6 Gravity interpretation 6.1 Time evolution under the SY
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