The coupled SYK model at finite temperature
- PDF / 1,459,758 Bytes
- 14 Pages / 595.276 x 841.89 pts (A4) Page_size
- 7 Downloads / 203 Views
Springer
Received: March 15, 2020 Accepted: May 9, 2020 Published: May 26, 2020
The coupled SYK model at finite temperature
a
Stanford Institute for Theoretical Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305, U.S.A. b Department of Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305, U.S.A. c Walter Burke Institute for Theoretical Physics, California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125, U.S.A. d Institute for Advanced Study, Tsinghua University, 30 Shuangqing Road, Beijing, 100084, China
E-mail: [email protected], [email protected] Abstract: Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS2 dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS 2 geometry. This geometry is an “eternal wormhole” because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function. Keywords: 1/N Expansion, Conformal Field Theory, Conformal and W Symmetry, 2D Gravity ArXiv ePrint: 2003.03916
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2020)129
JHEP05(2020)129
Xiao-Liang Qia,b and Pengfei Zhangc,d
Contents 1
2 Review of the coupled SYK model
2
3 Self-consistent equation for the spectral function
4
4 Spectral functions for small q
6
5 Spectral functions at large q
9
6 Conclusion
11
A Numerical details
11
1
Introduction
In general relativity, traversable wormholes are known to be forbidden by the average null energy condition (ANEC) [2, 3]. In a recent work, Gao, Jafferis and Wall [4] proposed that a traversable wormhole can be induced by turning on a coupling between the two boundaries of the (anti-de Sitter) eternal black hole geometry. The coupling is nonlocal from the bulk point of view, which makes it possible to violate the ANEC. From the boundary point of view (in the sense of holographic duality), the eternal black hole geometry corresponds to the thermal field double state [5, 6], which describes two entangled systems, each has a thermal reduced density matrix. The traversable wormhole describes the fact that scrambled quantum information in one system can be restored from the other system by making use of the coupling and the p
Data Loading...
