AdS/Condensed Matter Journal ClubReading List

The quantum entanglement has emerged as a central concept in the recentstudies of condensed matter physics and its holographic study in the contextof AdS/CFT. The purpose of this Journal Club is aimed to bring togetherthe condensed matter and high energy physics theorists who are interestedin exploring the perspectives of the interplay.

Therefore, we plan to focus on the issue of relating the MERA to theAdS geometry, and try to explore the possibility of deriving AdS bulk theoryfrom MERA. Since the entanglement entropy(EE) is key ingredient in thisstudy, it is also nice to review some basics of EE.

The plan of the AdS/Condensed Matter journal club is as follows. Foreach topic, we may spend 2 seminars on it:

1. Basics of EE

P. Calabrese and J. L. Cardy, Entanglement entropy and quan-tum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152].

P. Calabrese, J. Cardy, Entanglement entropy and conformalfield theory, J. Phys. A 42, 504005 (2009) [arXiv:0905.4013 [cond-mat]].

M. P. Hertzberg and F. Wilczek, Some Calculable Contributionsto Entanglement Entropy, Phys. Rev. Lett. 106 (2011) 050404[arXiv:1007.0993 [hep-th]].

T. Grover, A. Turner, A. Vishwanath, Entanglement Entropyof Gapped Phases and Topological Order in Three dimensions,Phys. Rev. B 84, 195120 (2011) [arXiv:1108.4038 [cond-mat]]

2. Holographic EE

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T. Takayanagi, Entanglement Entropy from a Holographic View-point, Class. Quant. Grav. 29, 153001 (2012) [arXiv:1204.2450[gr-qc]].

T. Nishioka, S. Ryu and T. Takayanagi, Holographic Entan-glement Entropy: An Overview, J. Phys. A 42, 504008 (2009)[arXiv:0905.0932 [hep-th]].

H. Liu and M. Mezei, A Refinement of entanglement entropy andthe number of degrees of freedom, arXiv:1202.2070 [hep-th].

A. Schwimmer and S. Theisen, Entanglement Entropy, TraceAnomalies and Holography, Nucl. Phys. B 801, 1 (2008) [arXiv:0802.1017 [hep-th]].

P. Hayden, M. Headrick and A. Maloney, Holographic MutualInformation is Monogamous, arXiv:1107.2940 [hep-th].

B. Czech, J. L. Karczmarek, F. Nogueira and M. Van Raamsdonk,The Gravity Dual of a Density Matrix, Class. Quant. Grav. 29(2012) 155009 [arXiv:1204.1330 [hep-th]].

V. Balasubramanian, M. B. McDermott and M. Van Raamsdonk,Momentum-space entanglement and renormalization in quantumfield theory, Phys. Rev. D 86 (2012) 045014 [arXiv:1108.3568[hep-th]].

3. Basics of MERA

G. Evenbly, and G. Vidal, Algorithms for entanglement renor-malization, Phys. Rev. B 79 (2009) 144108 [arXiv:0707.1454[cond-mat.str-el]].

G. Evenbly, and G. Vidal, Entanglement renormalization in freebosonic systems: real-space versus momentum-space renormal-ization group transforms, New J. Phys. 12, 025007 (2010)[arXiv:0801.2449 [quant-ph]].

F. Verstraete, J. I. Cirac, J. I. Latorre, E. Rico and M. M. Wolf,Renormalization group transformations on quantum states, Phys.Rev. Lett. 94 (2005) 140601 [quant-ph/0410227].

F. Verstraete, D. Porras, and J. I. Cirac, DMRG and periodicboundary conditions: a quantum information perspective, Phys.Rev. Lett. 93 (2004) 227205 [cond-mat/0404706].

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X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, Symmetry pro-tected topological orders and the group cohomology of their sym-metry group, arXiv:1106.4772 [cond-mat.str-el].

X. Chen, Z.-C. Gu, and X.-G. Wen, Local unitary transforma-tion, long-range quantum entanglement, wave function renormal-ization, and topological order, Phys. Rev. B 82, 155138 (2010)[arXiv:1004.3835 [cond-mat.str-el]].

4. AdS/MERA & cMERA

G. Evenbly, G. Vidal, Tensor Network States and Geometry,Journal of Statistical Physics, 145, pp 891-918 (2011) [rXiv:1106.1082[quant-ph]].

B. Swingle, Entanglement Renormalization and Holography, Phys.Rev. D 86, 065007 (2012) [arXiv:0905.1317 [cond-mat.str-el]].

B. Swingle, and T. Senthil, A geometric proof of the equalitybetween entanglement and edge spectra, Phys. Rev. B 86, 045117(2012) [arXiv:1109.1283 [cond-mat.str-el]].

B. Swingle, Constructing holographic spacetimes using entangle-ment renormalization, arXiv:1209.3304 [hep-th].

J. Haegeman, T. J. Osborne, H. Verschelde and F. Verstraete,Entanglement renormalization for quantum fields, arXiv:1102.5524[hep-th].

M. Nozaki, S. Ryu, and T. Takayanagi, Holographic Geometryof Entanglement Renormalization in Quantum Field Theories,arXiv:1208.3469.

M. R. Douglas, L. Mazzucato and S. S. Razamat, Holographicdual of free field theory, Phys. Rev. D 83 (2011) 071701 [arXiv:1011.4926[hep-th]].

X.L. Qis talk: http://online.itp.ucsb.edu/online/adscmt11/qi/

5. Quench of quantum entanglement

T. Hartman and J. Maldacena, Time Evolution of EntanglementEntropy from Black Hole Interiors, arXiv:1303.1080 [hep-th].

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V. E. Hubeny, M. Rangamani and E. Tonni, Thermalization ofCausal Holographic Information, arXiv:1302.0853 [hep-th].

P. Calabrese and J. Cardy, Quantum Quenches in Extended Sys-tems, J. Stat. Mech. 0706 (2007) P06008 [arXiv:0704.1880 [cond-mat.stat-mech]].

P. Calabrese, and J. Cardy, Evolution of Entanglement Entropyin One-Dimensional Systems, J. Stat. Mech. 0504 (2005) P04010[cond-mat/0503393].

M. Nozaki, T. Numasawa and T. Takayanagi, Holographic LocalQuenches and Entanglement Density, arXiv:1302.5703 [hep-th].

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