Abstract
In this paper, we present holographic descriptions of entanglement phase transition using AdS/BCFT. First, we analytically calculate the holographic pseudo entropy in the AdS/BCFT model with a brane localized scalar field and show the entanglement phase transition behavior where the time evolution of entropy changes from the linear growth to the trivial one via a critical logarithmic evolution. In this model, the imaginary valued scalar field localized on the brane controls the phase transition, which is analogous to the amount of projections in the measurement induced phase transition. Next, we study the AdS/BCFT model with a brane localized gauge field, where the phase transition looks different in that there is no logarithmically evolving critical point. Finally, we discuss a bulk analog of the above model by considering a double Wick rotation of the Janus solution. We compute the holographic pseudo entropy in this model and show that the entropy grows logarithmically.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Bombelli, R.K. Koul, J. Lee and R.D. Sorkin, A Quantum Source of Entropy for Black Holes, Phys. Rev. D 34 (1986) 373 [INSPIRE].
M. Srednicki, Entropy and area, Phys. Rev. Lett. 71 (1993) 666 [hep-th/9303048] [INSPIRE].
H. Casini and M. Huerta, Entanglement entropy in free quantum field theory, J. Phys. A 42 (2009) 504007 [arXiv:0905.2562] [INSPIRE].
P. Calabrese and J. Cardy, Entanglement entropy and conformal field theory, J. Phys. A 42 (2009) 504005 [arXiv:0905.4013] [INSPIRE].
G. Vidal, J.I. Latorre, E. Rico and A. Kitaev, Entanglement in quantum critical phenomena, Phys. Rev. Lett. 90 (2003) 227902 [quant-ph/0211074] [INSPIRE].
J.I. Latorre, E. Rico and G. Vidal, Ground state entanglement in quantum spin chains, Quant. Inf. Comput. 4 (2004) 48 [quant-ph/0304098] [INSPIRE].
M. Levin and X.-G. Wen, Detecting Topological Order in a Ground State Wave Function, Phys. Rev. Lett. 96 (2006) 110405 [cond-mat/0510613] [INSPIRE].
A. Kitaev and J. Preskill, Topological entanglement entropy, Phys. Rev. Lett. 96 (2006) 110404 [hep-th/0510092] [INSPIRE].
C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys. B 424 (1994) 443 [hep-th/9403108] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [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].
P. Calabrese and J. Cardy, Entanglement and correlation functions following a local quench: a conformal field theory approach, J. Stat. Mech. 0710 (2007) P10004 [arXiv:0708.3750] [INSPIRE].
B. Skinner, J. Ruhman and A. Nahum, Measurement-Induced Phase Transitions in the Dynamics of Entanglement, Phys. Rev. X 9 (2019) 031009 [arXiv:1808.05953] [INSPIRE].
Y. Li, X. Chen and M.P.A. Fisher, Quantum Zeno effect and the many-body entanglement transition, Phys. Rev. B 98 (2018) 205136 [arXiv:1808.06134] [INSPIRE].
K. Kawabata, T. Numasawa and S. Ryu, Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect, Phys. Rev. X 13 (2023) 021007 [arXiv:2206.05384] [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].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
A. Milekhin and F.K. Popov, Measurement-induced phase transition in teleportation and wormholes, arXiv:2210.03083 [INSPIRE].
S. Antonini, B. Grado-White, S.-K. Jian and B. Swingle, Holographic measurement and quantum teleportation in the SYK thermofield double, JHEP 02 (2023) 095 [arXiv:2211.07658] [INSPIRE].
S. Antonini et al., Holographic measurement and bulk teleportation, JHEP 12 (2022) 124 [arXiv:2209.12903] [INSPIRE].
K. Goto, M. Nozaki, K. Tamaoka and M.T. Tan, Entanglement dynamics of the non-unitary holographic channel, JHEP 03 (2023) 101 [arXiv:2211.03944] [INSPIRE].
S. Antonini, B. Grado-White, S.-K. Jian and B. Swingle, Holographic measurement in CFT thermofield doubles, JHEP 07 (2023) 014 [arXiv:2304.06743] [INSPIRE].
H. Kanda et al., AdS/BCFT with brane-localized scalar field, JHEP 03 (2023) 105 [arXiv:2302.03895] [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].
T. Hartman and J. Maldacena, Time Evolution of Entanglement Entropy from Black Hole Interiors, JHEP 05 (2013) 014 [arXiv:1303.1080] [INSPIRE].
Y. Nakata et al., New holographic generalization of entanglement entropy, Phys. Rev. D 103 (2021) 026005 [arXiv:2005.13801] [INSPIRE].
A. Mollabashi et al., Pseudo Entropy in Free Quantum Field Theories, Phys. Rev. Lett. 126 (2021) 081601 [arXiv:2011.09648] [INSPIRE].
A. Mollabashi et al., Aspects of pseudoentropy in field theories, Phys. Rev. Res. 3 (2021) 033254 [arXiv:2106.03118] [INSPIRE].
T. Nishioka, T. Takayanagi and Y. Taki, Topological pseudo entropy, JHEP 09 (2021) 015 [arXiv:2107.01797] [INSPIRE].
K. Goto, M. Nozaki and K. Tamaoka, Subregion spectrum form factor via pseudoentropy, Phys. Rev. D 104 (2021) L121902 [arXiv:2109.00372] [INSPIRE].
M. Miyaji, Island for gravitationally prepared state and pseudo entanglement wedge, JHEP 12 (2021) 013 [arXiv:2109.03830] [INSPIRE].
S. Murciano, P. Calabrese and R.M. Konik, Generalized entanglement entropies in two-dimensional conformal field theory, JHEP 05 (2022) 152 [arXiv:2112.09000] [INSPIRE].
J. Mukherjee, Pseudo Entropy in Υ(1) gauge theory, JHEP 10 (2022) 016 [arXiv:2205.08179] [INSPIRE].
Y. Ishiyama, R. Kojima, S. Matsui and K. Tamaoka, Notes on pseudo entropy amplification, PTEP 2022 (2022) 093B10 [arXiv:2206.14551] [INSPIRE].
W.-Z. Guo, S. He and Y.-X. Zhang, Constructible reality condition of pseudo entropy via pseudo-Hermiticity, JHEP 05 (2023) 021 [arXiv:2209.07308] [INSPIRE].
I. Akal et al., Page curve under final state projection, Phys. Rev. D 105 (2022) 126026 [arXiv:2112.08433] [INSPIRE].
I. Akal et al., Zoo of holographic moving mirrors, JHEP 08 (2022) 296 [arXiv:2205.02663] [INSPIRE].
W.-Z. Guo, S. He and Y.-X. Zhang, On the real-time evolution of pseudo-entropy in 2d CFTs, JHEP 09 (2022) 094 [arXiv:2206.11818] [INSPIRE].
K. Doi et al., Pseudoentropy in dS/CFT and Timelike Entanglement Entropy, Phys. Rev. Lett. 130 (2023) 031601 [arXiv:2210.09457] [INSPIRE].
Z. Li, Z.-Q. Xiao and R.-Q. Yang, On holographic time-like entanglement entropy, JHEP 04 (2023) 004 [arXiv:2211.14883] [INSPIRE].
K. Doi et al., Timelike entanglement entropy, JHEP 05 (2023) 052 [arXiv:2302.11695] [INSPIRE].
C.-S. Chu and H. Parihar, Time-like entanglement entropy in AdS/BCFT, JHEP 06 (2023) 173 [arXiv:2304.10907] [INSPIRE].
P.-Z. He and H.-Q. Zhang, Timelike Entanglement Entropy from Rindler Method, arXiv:2307.09803 [INSPIRE].
K. Narayan, de Sitter space, extremal surfaces, and time entanglement, Phys. Rev. D 107 (2023) 126004 [arXiv:2210.12963] [INSPIRE].
S. He, J. Yang, Y.-X. Zhang and Z.-X. Zhao, Pseudoentropy for descendant operators in two-dimensional conformal field theories, Phys. Rev. D 109 (2024) 025014 [arXiv:2301.04891] [INSPIRE].
K. Narayan and H.K. Saini, Notes on time entanglement and pseudo-entropy, arXiv:2303.01307 [INSPIRE].
X. Jiang, P. Wang, H. Wu and H. Yang, Timelike entanglement entropy in dS3/CFT2, JHEP 08 (2023) 216 [arXiv:2304.10376] [INSPIRE].
T. Kawamoto, S.-M. Ruan, Y.-K. Suzuki and T. Takayanagi, A half de Sitter holography, JHEP 10 (2023) 137 [arXiv:2306.07575] [INSPIRE].
D. Chen, X. Jiang and H. Yang, Holographic \(T\overline{T }\) deformed entanglement entropy in dS3/CFT2, Phys. Rev. D 109 (2024) 026011 [arXiv:2307.04673] [INSPIRE].
Z. Chen, Complex-valued Holographic Pseudo Entropy via Real-time AdS/CFT Correspondence, arXiv:2302.14303 [INSPIRE].
J. Chandra, Euclidean wormholes for individual 2d CFTs, arXiv:2305.07183 [INSPIRE].
S. Carignano, C.R. Marimón and L. Tagliacozzo, On temporal entropy and the complexity of computing the expectation value of local operators after a quench, arXiv:2307.11649 [INSPIRE].
A.J. Parzygnat, T. Takayanagi, Y. Taki and Z. Wei, SVD entanglement entropy, JHEP 12 (2023) 123 [arXiv:2307.06531] [INSPIRE].
W.-Z. Guo and J. Zhang, Sum rule for pseudo Rényi entropy, arXiv:2308.05261 [INSPIRE].
F. Omidi, Pseudo Rényi Entanglement Entropies For an Excited State and Its Time Evolution in a 2D CFT, arXiv:2309.04112 [INSPIRE].
K. Narayan, Further remarks on de Sitter space, extremal surfaces and time entanglement, arXiv:2310.00320 [INSPIRE].
C. Csaki and M. Reece, Toward a systematic holographic QCD: A Braneless approach, JHEP 05 (2007) 062 [hep-ph/0608266] [INSPIRE].
Y. Kim, B.-H. Lee, C. Park and S.-J. Sin, Gluon Condensation at Finite Temperature via AdS/CFT, JHEP 09 (2007) 105 [hep-th/0702131] [INSPIRE].
J. Erdmenger, C. Hoyos, A. O’Bannon and J. Wu, A Holographic Model of the Kondo Effect, JHEP 12 (2013) 086 [arXiv:1310.3271] [INSPIRE].
J. Erdmenger, M. Flory and M.-N. Newrzella, Bending branes for DCFT in two dimensions, JHEP 01 (2015) 058 [arXiv:1410.7811] [INSPIRE].
J. Erdmenger et al., Holographic impurities and Kondo effect, Fortsch. Phys. 64 (2016) 322 [arXiv:1511.09362] [INSPIRE].
J. Erdmenger et al., Entanglement Entropy in a Holographic Kondo Model, Fortsch. Phys. 64 (2016) 109 [arXiv:1511.03666] [INSPIRE].
K. Suzuki, Y.-K. Suzuki, T. Tsuda and M. Watanabe, Information metric on the boundary, JHEP 05 (2023) 013 [arXiv:2212.10899] [INSPIRE].
M. Miyaji and C. Murdia, Holographic BCFT with a Defect on the End-of-the-World brane, JHEP 11 (2022) 123 [arXiv:2208.13783] [INSPIRE].
S. Biswas, J. Kastikainen, S. Shashi and J. Sully, Holographic BCFT spectra from brane mergers, JHEP 11 (2022) 158 [arXiv:2209.11227] [INSPIRE].
Y. Kusuki and Z. Wei, AdS/BCFT from conformal bootstrap: construction of gravity with branes and particles, JHEP 01 (2023) 108 [arXiv:2210.03107] [INSPIRE].
A. Karch and L. Randall, Open and closed string interpretation of SUSY CFT’s on branes with boundaries, JHEP 06 (2001) 063 [hep-th/0105132] [INSPIRE].
J.L. Cardy, Boundary conformal field theory, hep-th/0411189 [INSPIRE].
I. Akal, Y. Kusuki, T. Takayanagi and Z. Wei, Codimension two holography for wedges, Phys. Rev. D 102 (2020) 126007 [arXiv:2007.06800] [INSPIRE].
L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with \(T\overline{T }\), JHEP 04 (2018) 010 [arXiv:1611.03470] [INSPIRE].
G.T. Horowitz and J.M. Maldacena, The black hole final state, JHEP 02 (2004) 008 [hep-th/0310281] [INSPIRE].
T. Shimaji, T. Takayanagi and Z. Wei, Holographic Quantum Circuits from Splitting/Joining Local Quenches, JHEP 03 (2019) 165 [arXiv:1812.01176] [INSPIRE].
P. Caputa et al., Double Local Quenches in 2D CFTs and Gravitational Force, JHEP 09 (2019) 018 [arXiv:1905.08265] [INSPIRE].
Y. Kusuki, K. Tamaoka, Z. Wei and Y. Yoneta, Efficient Simulation of Low Temperature Physics in One-Dimensional Gapless Systems, arXiv:2309.02519 [INSPIRE].
A. Castro, D. Grumiller, F. Larsen and R. McNees, Holographic Description of AdS(2) Black Holes, JHEP 11 (2008) 052 [arXiv:0809.4264] [INSPIRE].
D. Bak, M. Gutperle and S. Hirano, A dilatonic deformation of AdS(5) and its field theory dual, JHEP 05 (2003) 072 [hep-th/0304129] [INSPIRE].
A.B. Clark, D.Z. Freedman, A. Karch and M. Schnabl, Dual of the Janus solution: An interface conformal field theory, Phys. Rev. D 71 (2005) 066003 [hep-th/0407073] [INSPIRE].
D. Bak, M. Gutperle and S. Hirano, Three dimensional Janus and time-dependent black holes, JHEP 02 (2007) 068 [hep-th/0701108] [INSPIRE].
T. Azeyanagi, A. Karch, T. Takayanagi and E.G. Thompson, Holographic calculation of boundary entropy, JHEP 03 (2008) 054 [arXiv:0712.1850] [INSPIRE].
A. Karch, Z.-X. Luo and H.-Y. Sun, Universal relations for holographic interfaces, JHEP 09 (2021) 172 [arXiv:2107.02165] [INSPIRE].
M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].
D. Bak, A. Gustavsson and S.-J. Rey, Conformal Janus on Euclidean Sphere, JHEP 12 (2016) 025 [arXiv:1605.00857] [INSPIRE].
J. Estes et al., On Holographic Defect Entropy, JHEP 05 (2014) 084 [arXiv:1403.6475] [INSPIRE].
M. Gutperle and A. Trivella, Note on entanglement entropy and regularization in holographic interface theories, Phys. Rev. D 95 (2017) 066009 [arXiv:1611.07595] [INSPIRE].
https://functions.wolfram.com/EllipticIntegrals/EllipticPi3/17/01/.
T. Sagawa and M. Ueda, Quantum measurement and Quantum Control, second edition, SAIENSU — SHA Co. Ltd. (2022).
H.P. Breuer and F. Petruccione, The theory of open quantum systems, Oxford University Press, Great Clarendon Street (2002) [https://doi.org/10.1093/acprof:oso/9780199213900.001.0001].
A.O. Caldeira and A.J. Leggett, Path integral approach to quantum Brownian motion, Physica A 121 (1983) 587 [INSPIRE].
R.P. Feynman and F.L. Vernon Jr., The theory of a general quantum system interacting with a linear dissipative system, Annals Phys. 24 (1963) 118 [INSPIRE].
M. Gutperle and A. Strominger, Space-like branes, JHEP 04 (2002) 018 [hep-th/0202210] [INSPIRE].
Acknowledgments
We are grateful to Rathindra Nath Das, Juan Maldacena, Shinsei Ryu and Mark Van Raamsdonk for useful discussions. This work is supported by MEXT KAKENHI Grant-in-Aid for Transformative Research Areas (A) through the “Extreme Universe” collaboration: Grant Number 21H05187. This work is also supported by Inamori Research Institute for Science and by JSPS Grant-in-Aid for Scientific Research (A) No. 21H04469. TK is supported by Grant-in-Aid for JSPS Fellows No. 23KJ1315. YS is supported by Grant-in-Aid for JSPS Fellows No.23KJ1337. ZW is supported by the Society of Fellows at Harvard University.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2311.13201
Rights and permissions
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.
About this article
Cite this article
Kanda, H., Kawamoto, T., Suzuki, Yk. et al. Entanglement phase transition in holographic pseudo entropy. J. High Energ. Phys. 2024, 60 (2024). https://doi.org/10.1007/JHEP03(2024)060
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2024)060