Abstract
A simple but quite non-trivial class of non-equilibrium processes of a quantum many-body system is quantum quenches. We start with a ground state \(\mid \!\Phi _{0}\rangle\) of a certain Hamiltonian H 0. At time tâ=â0, we suddenly change the Hamiltonian from H 0 to a new one H. The original state \(\mid \!\Phi _{0}\rangle\) no longer stays at the ground state and starts to experience the time evolution for tâ>â0. Such a process is called a quantum quench. In particular, when the Hamiltonian changes homogeneously over the whole space, it is called a global quench [131, 132, 133], while if the change is localized in a certain small region, it is called a local quench [134].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
This illustrates an important fact: while the overall spatial volume inside a black hole shrinks to zero, areas of spatial sections actually continue to grow. This has been conjectured to be related to the growth of complexity of the state [157].
References
V.E. Hubeny, M. Rangamani, T. Takayanagi, A Covariant holographic entanglement entropy proposal. J. High Energy Phys. 0707, 062 (2007). arXiv:0705.0016 [hep-th]
R. Wald, General Relativity (University of Chicago Press, Chicago, 1984)
V.E. Hubeny, H. Maxfield, M. Rangamani, E. Tonni, Holographic entanglement plateaux. J. High Energy Phys. 1308, 092 (2013). arXiv:1306.4004
V.E. Hubeny, Extremal surfaces as bulk probes in AdS/CFT. J. High Energy Phys. 07, 093 (2012). arXiv:1203.1044 [hep-th]
P. Calabrese, J. Cardy, Evolution of entanglement entropy in one-dimensional systems. J. Stat. Mech. 04, 10 (2005). cond-mat/0503393. http://arxiv.org/abs/cond-mat/0503393
P. Calabrese, J. Cardy, Time-dependence of correlation functions following a quantum quench. Phys. Rev. Lett. 96, 136801 (2006). cond-mat/0601225. http://arxiv.org/abs/cond-mat/0601225
P. Calabrese, J. Cardy, Quantum quenches in extended systems. J. Stat. Mech. 6, 8 (2007). arXiv:0704.1880 [cond-mat.stat-mech]
P. Calabrese, J. Cardy, Entanglement and correlation functions following a local quench: a conformal field theory approach. J. Stat. Mech. 10, 4 (2007). arXiv:0708.3750 [cond-mat.stat-mech]
J.M. Deutsch, Quantum statistical mechanics in a closed system. Phys. Rev. A 43, 2046â2049 (1991)
M. Srednicki, Chaos and quantum thermalization. Phys. Rev. E 50, 888â901 (1994). cond-mat/9403051
S.R. Das, D.A. Galante, R.C. Myers, Smooth and fast versus instantaneous quenches in quantum field theory. J. High Energy Phys. 08, 073 (2015). arXiv:1505.05224 [hep-th]
J. Cardy, Quantum quenches to a critical point in one dimension: some further results (2015). arXiv:1507.07266 [cond-mat.stat-mech]
G. Mandal, R. Sinha, N. Sorokhaibam, Thermalization with chemical potentials, and higher spin black holes. J. High Energy Phys. 08, 013 (2015). arXiv:1501.04580 [hep-th]
T. Takayanagi, T. Ugajin, Measuring black hole formations by entanglement entropy via coarse-graining. J. High Energy Phys. 1011, 054 (2010). arXiv:1008.3439 [hep-th]
T. Hartman, J. Maldacena, Time evolution of entanglement entropy from black hole interiors. J. High Energy Phys. 1305, 014 (2013). arXiv:1303.1080 [hep-th]
N. Ishibashi, The boundary and crosscap states in conformal field theories. Mod. Phys. Lett. A4, 251 (1989).
J.L. Cardy, Boundary conditions, fusion rules and the Verlinde formula. Nucl. Phys. B324, 581 (1989)
A. Mollabashi, M. Nozaki, S. Ryu, T. Takayanagi, Holographic geometry of cMERA for quantum quenches and finite temperature. J. High Energy Phys. 1403, 098 (2014). arXiv:1311.6095 [hep-th]
L.A. Pando Zayas, N. Quiroz, Left-right entanglement entropy of boundary states. J. High Energy Phys. 1501, 110 (2015). arXiv:1407.7057 [hep-th]
M. Miyaji, S. Ryu, T. Takayanagi, X. Wen, Boundary states as holographic duals of trivial spacetimes. J. High Energy Phys. 05, 152 (2015). arXiv:1412.6226 [hep-th]
C.T. Asplund, A. Bernamonti, F. Galli, T. Hartman, Entanglement scrambling in 2D conformal field theory. J. High Energy Phys. 09, 110 (2015). arXiv:1506.03772 [hep-th]
L. Fidkowski, V. Hubeny, M. Kleban, S. Shenker, The black hole singularity in AdS / CFT. J. High Energy Phys. 02, 014 (2004). arXiv:hep-th/0306170 [hep-th]
J.M. Maldacena, Eternal black holes in anti-de Sitter. J. High Energy Phys. 0304, 021 (2003). arXiv:hep-th/0106112 [hep-th]
J. Abajo-Arrastia, J. Aparicio, E. Lopez, Holographic evolution of entanglement entropy. J. High Energy Phys. 1011, 149 (2010). arXiv:1006.4090 [hep-th]
V. Balasubramanian, A. Bernamonti, J. de Boer, N. Copland, B. Craps, et al., Thermalization of strongly coupled field theories. Phys. Rev. Lett. 106, 191601 (2011). arXiv:1012.4753 [hep-th]
V. Balasubramanian, A. Bernamonti, J. de Boer, N. Copland, B. Craps, et al., Holographic thermalization. Phys. Rev. D84, 026010 (2011). arXiv:1103.2683 [hep-th]
V.E. Hubeny, H. Maxfield, Holographic probes of collapsing black holes. J. High Energy Phys. 03, 097 (2014). arXiv:1312.6887 [hep-th]
V.E. Hubeny, Precursors see inside black holes. Int. J. Mod. Phys. D12, 1693â1698 (2003). arXiv:hep-th/0208047 [hep-th]
T. Takayanagi, Holographic dual of BCFT. Phys. Rev. Lett. 107, 101602 (2011). arXiv:1105.5165 [hep-th]
H. Liu, S.J. Suh, Entanglement tsunami: universal scaling in holographic thermalization. Phys. Rev. Lett. 112, 011601 (2014). arXiv:1305.7244 [hep-th]
L. Susskind, Computational complexity and black hole horizons. Fortschr. Phys. 64, 24â43 (2016). arXiv:1403.5695 [hep-th]
H. Liu, S.J. Suh, Entanglement growth during thermalization in holographic systems. Phys. Rev. D89 (6), 066012 (2014). arXiv:1311.1200 [hep-th]
V.E. Hubeny, M. Rangamani, E. Tonni, Thermalization of causal holographic information. J. High Energy Phys. 05, 136 (2013). arXiv:1302.0853 [hep-th]
T. Hartman, N. Afkhami-Jeddi, Speed limits for entanglement (2015). arXiv:1512.02695 [hep-th]
H. Casini, H. Liu, M. Mezei, Spread of entanglement and causality. J. High Energy Phys. 07, 077 (2016). arXiv:1509.05044 [hep-th]
S.H. Shenker, D. Stanford, Black holes and the butterfly effect. J. High Energy Phys. 03, 067 (2014). arXiv:1306.0622 [hep-th]
E.H. Lieb, D.W. Robinson, The finite group velocity of quantum spin systems. Commun. Math. Phys. 28, 251â257 (1972)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
Âİ 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Rangamani, M., Takayanagi, T. (2017). Quantum Quenches and Entanglement. In: Holographic Entanglement Entropy. Lecture Notes in Physics, vol 931. Springer, Cham. https://doi.org/10.1007/978-3-319-52573-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-52573-0_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-52571-6
Online ISBN: 978-3-319-52573-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)