Abstract
We study the time evolution of cMERA (continuous MERA) under quantum quenches in free field theories. We calculate the corresponding holographic metric using the proposal in arXiv:1208.3469 and confirm that it qualitatively agrees with its gravity dual given by a half of the AdS black hole spacetime, argued by Hartman and Maldacena in arXiv:1303.1080. By doubling the cMERA for the quantum quench, we give an explicit construction of finite temperature cMERA. We also study cMERA in the presence of chemical potential and show that there is an enhancement of metric in the infrared region corresponding to the Fermi energy.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
G. ’t Hooft, Dimensional reduction in quantum gravity, gr-qc/9310026 [INSPIRE].
L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].
D. Bigatti and L. Susskind, TASI lectures on the holographic principle, hep-th/0002044 [INSPIRE].
G. Vidal, Entanglement renormalization, Phys. Rev. Lett. 99 (2007) 220405, cond-mat/0512165.
G. Vidal, Entanglement Renormalization: an introduction, arXiv:0912.1651.
G. Evenbly and G. Vidal, Quantum Criticality with the Multi-scale Entanglement Renormalization Ansatz, arXiv:1109.5334.
B. Swingle, Entanglement Renormalization and Holography, Phys. Rev. D 86 (2012) 065007 [arXiv:0905.1317] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
T. Nishioka, S. Ryu and T. Takayanagi, Holographic Entanglement Entropy: An Overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932] [INSPIRE].
T. Takayanagi, Entanglement Entropy from a Holographic Viewpoint, Class. Quant. Grav. 29 (2012) 153001 [arXiv:1204.2450] [INSPIRE].
M. Van Raamsdonk, Comments on quantum gravity and entanglement, arXiv:0907.2939 [INSPIRE].
M. Van Raamsdonk, Building up spacetime with quantum entanglement, Gen. Rel. Grav. 42 (2010) 2323 [Int. J. Mod. Phys. D 19 (2010) 2429] [arXiv:1005.3035] [INSPIRE].
M. Nozaki, S. Ryu and T. Takayanagi, Holographic geometry of entanglement renormalization in quantum field theories, JHEP 10 (2012) 193 [arXiv:1208.3469] [INSPIRE].
J. Haegeman, T.J. Osborne, H. Verschelde and F. Verstraete, Entanglement Renormalization for Quantum Fields in Real Space, Phys. Rev. Lett. 110 (2013) 100402 [arXiv:1102.5524] [INSPIRE].
J. Molina-Vilaplana and P. Sodano, Holographic view on quantum correlations and mutual information between disjoint blocks of a quantum critical system, JHEP 10 (2011) 011 [arXiv:1108.1277] [INSPIRE].
J. Molina-Vilaplana, Connecting Entanglement Renormalization and Gauge/Gravity dualities, arXiv:1109.5592 [INSPIRE].
J. Molina-Vilaplana, Holographic entanglement entropy of AdS solitons and tensor network states, JHEP 05 (2013) 024 [arXiv:1210.6759] [INSPIRE].
V. Balasubramanian, M.B. McDermott and M. Van Raamsdonk, Momentum-space entanglement and renormalization in quantum field theory, Phys. Rev. D 86 (2012) 045014 [arXiv:1108.3568] [INSPIRE].
H. Matsueda, M. Ishihara and Y. Hashizume, Tensor network and a black hole, Phys. Rev. D 87 (2013) 066002 [arXiv:1208.0206] [INSPIRE].
H. Matsueda, Multiscale Entanglement Renormalization Ansatz for Kondo Problem, arXiv:1208.2872 [INSPIRE].
B. Swingle, Constructing holographic spacetimes using entanglement renormalization, arXiv:1209.3304 [INSPIRE].
G. Evenbly and G. Vidal, A theory of minimal updates in holography, arXiv:1307.0831 [INSPIRE].
X.-L. Qi, Exact holographic mapping and emergent space-time geometry, arXiv:1309.6282 [INSPIRE].
S.-S. Lee, Quantum renormalization group and holography, JHEP 01 (2014) 076 [arXiv:1305.3908] [INSPIRE].
T. Hartman and J. Maldacena, Time evolution of entanglement entropy from black hole interiors, JHEP 05 (2013) 014 [arXiv:1303.1080] [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
P. Calabrese and J.L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 0504 (2005) P04010 [cond-mat/0503393] [INSPIRE].
H. Liu and S.J. Suh, Entanglement Tsunami: Universal Scaling in Holographic Thermalization, Phys. Rev. Lett. 112 (2014) 011601 [arXiv:1305.7244] [INSPIRE].
J. Abajo-Arrastia, J. Aparicio and E. Lopez, Holographic evolution of entanglement entropy, JHEP 11 (2010) 149 [arXiv:1006.4090] [INSPIRE].
T. Albash and C.V. Johnson, Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches, New J. Phys. 13 (2011) 045017 [arXiv:1008.3027] [INSPIRE].
T. Takayanagi and T. Ugajin, Measuring black hole formations by entanglement entropy via Coarse-Graining, JHEP 11 (2010) 054 [arXiv:1008.3439] [INSPIRE].
V. Balasubramanian et al., Thermalization of strongly coupled field theories, Phys. Rev. Lett. 106 (2011) 191601 [arXiv:1012.4753] [INSPIRE].
V. Balasubramanian et al., Holographic Thermalization, Phys. Rev. D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].
D. Galante and M. Schvellinger, Thermalization with a chemical potential from AdS spaces, JHEP 07 (2012) 096 [arXiv:1205.1548] [INSPIRE].
E. Caceres and A. Kundu, Holographic thermalization with chemical potential, JHEP 09 (2012) 055 [arXiv:1205.2354] [INSPIRE].
I. Affleck and A.W. Ludwig, Universal noninteger ’ground state degeneracy’ in critical quantum systems, Phys. Rev. Lett. 67 (1991) 161 [INSPIRE].
T. Takayanagi, Holographic Dual of BCFT, Phys. Rev. Lett. 107 (2011) 101602 [arXiv:1105.5165] [INSPIRE].
M. Fujita, T. Takayanagi and E. Tonni, Aspects of AdS/BCFT, JHEP 11 (2011) 043 [arXiv:1108.5152] [INSPIRE].
P. Calabrese and J. Cardy, Entanglement and correlation functions following a local quench: a conformal field theory approach, J. Stat. Mech. (2007) P10004 [arXiv:0708.3750].
M.M. Roberts, Time evolution of entanglement entropy from a pulse, JHEP 12 (2012) 027 [arXiv:1204.1982] [INSPIRE].
M. Nozaki, T. Numasawa and T. Takayanagi, Holographic local quenches and entanglement density, JHEP 05 (2013) 080 [arXiv:1302.5703] [INSPIRE].
T. Ugajin, Two dimensional quantum quenches and holography, arXiv:1311.2562 [INSPIRE].
C.T. Asplund and A. Bernamonti, Mutual information after a local quench in conformal field theory, arXiv:1311.4173 [INSPIRE].
J. Bhattacharya, M. Nozaki, T. Takayanagi and T. Ugajin, Thermodynamical Property of Entanglement Entropy for Excited States, Phys. Rev. Lett. 110 (2013) 091602 [arXiv:1212.1164] [INSPIRE].
P. Caputa, G. Mandal and R. Sinha, Dynamical entanglement entropy with angular momentum and U(1) charge, JHEP 11 (2013) 052 [arXiv:1306.4974] [INSPIRE].
G. Wong, I. Klich, L.A. Pando Zayas and D. Vaman, Entanglement temperature and entanglement entropy of excited states, JHEP 12 (2013) 020 [arXiv:1305.3291] [INSPIRE].
D.D. Blanco, H. Casini, L.-Y. Hung and R.C. Myers, Relative entropy and holography, JHEP 08 (2013) 060 [arXiv:1305.3182] [INSPIRE].
D. Allahbakhshi, M. Alishahiha and A. Naseh, Entanglement thermodynamics, JHEP 08 (2013) 102 [arXiv:1305.2728] [INSPIRE].
W.-z. Guo, S. He and J. Tao, Note on entanglement temperature for low thermal excited states in higher derivative gravity, JHEP 08 (2013) 050 [arXiv:1305.2682] [INSPIRE].
M. Nozaki, T. Numasawa, A. Prudenziati and T. Takayanagi, Dynamics of Entanglement Entropy from Einstein Equation, Phys. Rev. D 88 (2013) 026012 [arXiv:1304.7100] [INSPIRE].
J. Bhattacharya and T. Takayanagi, Entropic counterpart of perturbative Einstein equation, JHEP 10 (2013) 219 [arXiv:1308.3792] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1311.6095
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Mollabashi, A., Naozaki, M., Ryu, S. et al. Holographic geometry of cMERA for quantum quenches and finite temperature. J. High Energ. Phys. 2014, 98 (2014). https://doi.org/10.1007/JHEP03(2014)098
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2014)098