Abstract
We explore the efficacy of entanglement entropy as a tool for detecting thermal phase transitions in a family of gauge theories described holographically. The rich phase diagram of these theories encompasses first and second-order phase transitions, as well as a critical and a triple point. While entanglement measures demonstrate some success in probing transitions between plasma phases, they prove inadequate when applied to phase transitions leading to gapped phases. Nonetheless, entanglement measures excel in accurately determining the critical exponent associated with the observed phase transitions, providing valuable insight into the critical behavior of these systems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
I.R. Klebanov, D. Kutasov and A. Murugan, Entanglement as a probe of confinement, Nucl. Phys. B 796 (2008) 274 [arXiv:0709.2140] [INSPIRE].
U. Kol et al., Confinement, phase transitions and non-locality in the entanglement entropy, JHEP 06 (2014) 005 [arXiv:1403.2721] [INSPIRE].
C. Nunez, M. Oyarzo and R. Stuardo, Confinement in (1 + 1) dimensions: a holographic perspective from I-branes, JHEP 09 (2023) 201 [arXiv:2307.04783] [INSPIRE].
N. Jokela and J.G. Subils, Is entanglement a probe of confinement?, JHEP 02 (2021) 147 [arXiv:2010.09392] [INSPIRE].
N. Jokela, J.M. Penín, A.V. Ramallo and D. Zoakos, Gravity dual of a multilayer system, JHEP 03 (2019) 064 [arXiv:1901.02020] [INSPIRE].
H. Casini, J.M. Magan and P.J. Martinez, Entropic order parameters in weakly coupled gauge theories, JHEP 01 (2022) 079 [arXiv:2110.02980] [INSPIRE].
A.G. Moghaddam, K. Pöyhönen and T. Ojanen, Exponential shortcut to measurement-induced entanglement phase transitions, Phys. Rev. Lett. 131 (2023) 020401 [arXiv:2302.14044] [INSPIRE].
A. Velytsky, Entanglement entropy in SU(N) gauge theory, PoS LATTICE2008 (2008) 256 [arXiv:0809.4502] [INSPIRE].
P.V. Buividovich and M.I. Polikarpov, Numerical study of entanglement entropy in SU(2) lattice gauge theory, Nucl. Phys. B 802 (2008) 458 [arXiv:0802.4247] [INSPIRE].
Y. Nakagawa, A. Nakamura, S. Motoki and V.I. Zakharov, Entanglement entropy of SU(3) Yang-Mills theory, PoS LAT2009 (2009) 188 [arXiv:0911.2596] [INSPIRE].
Y. Nakagawa, A. Nakamura, S. Motoki and V.I. Zakharov, Quantum entanglement in SU(3) lattice Yang-Mills theory at zero and finite temperatures, PoS LATTICE2010 (2010) 281 [arXiv:1104.1011] [INSPIRE].
E. Itou et al., Entanglement in four-dimensional SU(3) gauge theory, PTEP 2016 (2016) 061B01 [arXiv:1512.01334] [INSPIRE].
A. Rabenstein, N. Bodendorfer, P. Buividovich and A. Schäfer, Lattice study of Rényi entanglement entropy in SU(Nc) lattice Yang-Mills theory with Nc = 2, 3, 4, Phys. Rev. D 100 (2019) 034504 [arXiv:1812.04279] [INSPIRE].
T. Rindlisbacher et al., Improved lattice method for determining entanglement measures in SU(N) gauge theories, PoS LATTICE2022 (2022) 031 [arXiv:2211.00425] [INSPIRE].
A. Bulgarelli and M. Panero, Entanglement entropy from non-equilibrium Monte Carlo simulations, JHEP 06 (2023) 030 [arXiv:2304.03311] [INSPIRE].
N. Jokela et al., Progress in the lattice evaluation of entanglement entropy of three-dimensional Yang-Mills theories and holographic bulk reconstruction, JHEP 12 (2023) 137 [arXiv:2304.08949] [INSPIRE].
A. Bulgarelli and M. Panero, Entanglement entropy from non-equilibrium lattice simulations, in the proceedings of the 40th International Symposium on Lattice Field Theory, (2023) [arXiv:2309.15480] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
J. Knaute and B. Kämpfer, Holographic entanglement entropy in the QCD phase diagram with a critical point, Phys. Rev. D 96 (2017) 106003 [arXiv:1706.02647] [INSPIRE].
M. Asadi, B. Amrahi and H. Eshaghi-Kenari, Probing phase structure of strongly coupled matter with holographic entanglement measures, Eur. Phys. J. C 83 (2023) 69 [arXiv:2209.01586] [INSPIRE].
H. Gong et al., Diagnosing quantum phase transitions via holographic entanglement entropy at finite temperature, Eur. Phys. J. C 83 (2023) 1042 [arXiv:2306.05096] [INSPIRE].
X.-X. Zeng and L.-F. Li, Holographic phase transition probed by nonlocal observables, Adv. High Energy Phys. 2016 (2016) 6153435 [arXiv:1609.06535] [INSPIRE].
S.-J. Zhang, Holographic entanglement entropy close to crossover/phase transition in strongly coupled systems, Nucl. Phys. B 916 (2017) 304 [arXiv:1608.03072] [INSPIRE].
M. Baggioli and D. Giataganas, Detecting topological quantum phase transitions via the c-function, Phys. Rev. D 103 (2021) 026009 [arXiv:2007.07273] [INSPIRE].
M. Baggioli, Y. Liu and X.-M. Wu, Entanglement entropy as an order parameter for strongly coupled nodal line semimetals, JHEP 05 (2023) 221 [arXiv:2302.11096] [INSPIRE].
Y. Ling et al., Holographic entanglement entropy close to quantum phase transitions, JHEP 04 (2016) 114 [arXiv:1502.03661] [INSPIRE].
Y. Ling, P. Liu and J.-P. Wu, Characterization of quantum phase transition using holographic entanglement entropy, Phys. Rev. D 93 (2016) 126004 [arXiv:1604.04857] [INSPIRE].
D. Elander, A.F. Faedo, D. Mateos and J.G. Subils, Phase transitions in a three-dimensional analogue of Klebanov-Strassler, JHEP 06 (2020) 131 [arXiv:2002.08279] [INSPIRE].
A.F. Faedo, D. Mateos, D. Pravos and J.G. Subils, Mass gap without confinement, JHEP 06 (2017) 153 [arXiv:1702.05988] [INSPIRE].
R. Bryand and S. Salamon, On the construction of some complete metrices with expectional holonomy, Duke Math. J. 58 (1989) 829 [INSPIRE].
G.W. Gibbons, D.N. Page and C.N. Pope, Einstein metrics on S3R3 and R4 bundles, Commun. Math. Phys. 127 (1990) 529 [INSPIRE].
M. Cvetic, G.W. Gibbons, H. Lu and C.N. Pope, Supersymmetric nonsingular fractional D2 branes and NS NS 2 branes, Nucl. Phys. B 606 (2001) 18 [hep-th/0101096] [INSPIRE].
M. Cvetic, G.W. Gibbons, H. Lu and C.N. Pope, New cohomogeneity one metrics with Spin(7) holonomy, J. Geom. Phys. 49 (2004) 350 [math/0105119] [INSPIRE].
M. Cvetic, G.W. Gibbons, H. Lu and C.N. Pope, New complete noncompact Spin(7) manifolds, Nucl. Phys. B 620 (2002) 29 [hep-th/0103155] [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: duality cascades and χSB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
A. Loewy and Y. Oz, Branes in special holonomy backgrounds, Phys. Lett. B 537 (2002) 147 [hep-th/0203092] [INSPIRE].
I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
D. Elander et al., Mass spectrum of gapped, non-confining theories with multi-scale dynamics, JHEP 05 (2019) 175 [arXiv:1810.04656] [INSPIRE].
H. Ooguri and C.-S. Park, Superconformal Chern-Simons theories and the squashed seven sphere, JHEP 11 (2008) 082 [arXiv:0808.0500] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
A. Hashimoto, S. Hirano and P. Ouyang, Branes and fluxes in special holonomy manifolds and cascading field theories, JHEP 06 (2011) 101 [arXiv:1004.0903] [INSPIRE].
I. Bena et al., Holographic dual of hot Polchinski-Strassler quark-gluon plasma, JHEP 09 (2019) 033 [arXiv:1805.06463] [INSPIRE].
S.W. Hawking and D.N. Page, Thermodynamics of black holes in anti-de Sitter space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].
S. Bilson, Extracting spacetimes using the AdS/CFT conjecture. Part II, JHEP 02 (2011) 050 [arXiv:1012.1812] [INSPIRE].
N. Jokela and A. Pönni, Towards precision holography, Phys. Rev. D 103 (2021) 026010 [arXiv:2007.00010] [INSPIRE].
M. Headrick, Entanglement Rényi entropies in holographic theories, Phys. Rev. D 82 (2010) 126010 [arXiv:1006.0047] [INSPIRE].
K. Bhattacharya, B.R. Majhi and S. Samanta, Van der Waals criticality in AdS black holes: a phenomenological study, Phys. Rev. D 96 (2017) 084037 [arXiv:1709.02650] [INSPIRE].
L.G. Yaffe, Large n limits as classical mechanics, Rev. Mod. Phys. 54 (1982) 407 [INSPIRE].
N. Evans, K. Jensen and K.-Y. Kim, Non mean-field quantum critical points from holography, Phys. Rev. D 82 (2010) 105012 [arXiv:1008.1889] [INSPIRE].
E. Conde and A.V. Ramallo, On the gravity dual of Chern-Simons-matter theories with unquenched flavor, JHEP 07 (2011) 099 [arXiv:1105.6045] [INSPIRE].
N. Jokela, J. Mas, A.V. Ramallo and D. Zoakos, Thermodynamics of the brane in Chern-Simons matter theories with flavor, JHEP 02 (2013) 144 [arXiv:1211.0630] [INSPIRE].
A.F. Faedo, C. Hoyos and J.G. Subils, Monopoles and confinement in three dimensions from holography, JHEP 03 (2023) 218 [arXiv:2212.04996] [INSPIRE].
A. van Niekerk, Entanglement entropy in nonconformal holographic theories, arXiv:1108.2294 [INSPIRE].
N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].
Acknowledgments
We thank Antón Faedo for valuable discussions. J. S. thanks the possibility for participating in the PiTP 2023 program: “Understanding Confinement” in the last stages of this project. There, he enjoyed discussions on the topic of entanglement entropy as a probe of confinement with Andrea Bulgarelli, Igor Klebanov, and Pedro Jorge Martinez, to whom he is truly thankful. Nordita is supported in part by NordForsk. H. R. is supported in part by the Finnish Cultural Foundation.
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: 2310.11205
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
Jokela, N., Ruotsalainen, H. & Subils, J.G. Limitations of entanglement entropy in detecting thermal phase transitions. J. High Energ. Phys. 2024, 186 (2024). https://doi.org/10.1007/JHEP01(2024)186
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2024)186