Time dependence of entanglement entropy on the fuzzy sphere. (English) Zbl 1381.83083
Summary: We numerically study the behaviour of entanglement entropy for a free scalar field on the noncommutative (“fuzzy”) sphere after a mass quench. It is known that the entanglement entropy before a quench violates the usual area law due to the non-local nature of the theory. By comparing our results to the ordinary sphere, we find results that, despite this non-locality, are compatible with entanglement being spread by ballistic propagation of entangled quasi-particles at a speed no greater than the speed of light. However, we also find that, when the pre-quench mass is much larger than the inverse of the short-distance cutoff of the fuzzy sphere (a regime with no commutative analogue), the entanglement entropy spreads faster than allowed by a local model.
MSC:
| 83C65 | Methods of noncommutative geometry in general relativity |
| 81R60 | Noncommutative geometry in quantum theory |
| 94A17 | Measures of information, entropy |
References:
| [1] | S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett.96 (2006) 181602 [hep-th/0603001] [INSPIRE]. · Zbl 1228.83110 · doi:10.1103/PhysRevLett.96.181602 |
| [2] | V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP07 (2007) 062 [arXiv:0705.0016] [INSPIRE]. · doi:10.1088/1126-6708/2007/07/062 |
| [3] | H. Liu and S.J. Suh, Entanglement tsunami: universal scaling in holographic thermalization, Phys. Rev. Lett.112 (2014) 011601 [arXiv:1305.7244] [INSPIRE]. · doi:10.1103/PhysRevLett.112.011601 |
| [4] | P. Calabrese and J.L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech.0504 (2005) P04010 [cond-mat/0503393] [INSPIRE]. · Zbl 1456.82578 |
| [5] | S. Kundu and J.F. Pedraza, Spread of entanglement for small subsystems in holographic CFTs, Phys. Rev.D 95 (2017) 086008 [arXiv:1602.05934] [INSPIRE]. |
| [6] | H. Casini, H. Liu and M. Mezei, Spread of entanglement and causality, JHEP07 (2016) 077 [arXiv:1509.05044] [INSPIRE]. · Zbl 1390.83092 · doi:10.1007/JHEP07(2016)077 |
| [7] | J.S. Cotler, M.P. Hertzberg, M. Mezei and M.T. Mueller, Entanglement growth after a global quench in free scalar field theory, JHEP11 (2016) 166 [arXiv:1609.00872] [INSPIRE]. · doi:10.1007/JHEP11(2016)166 |
| [8] | N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP09 (1999) 032 [hep-th/9908142] [INSPIRE]. · Zbl 0957.81085 · doi:10.1088/1126-6708/1999/09/032 |
| [9] | D. Bigatti and L. Susskind, Magnetic fields, branes and noncommutative geometry, Phys. Rev.D 62 (2000) 066004 [hep-th/9908056] [INSPIRE]. |
| [10] | Y. Sekino and L. Susskind, Fast scramblers, JHEP10 (2008) 065 [arXiv:0808.2096] [INSPIRE]. · doi:10.1088/1126-6708/2008/10/065 |
| [11] | N. Lashkari, D. Stanford, M. Hastings, T. Osborne and P. Hayden, Towards the fast scrambling conjecture, JHEP04 (2013) 022 [arXiv:1111.6580] [INSPIRE]. · Zbl 1342.81374 · doi:10.1007/JHEP04(2013)022 |
| [12] | L. Brady and V. Sahakian, Scrambling with matrix black holes, Phys. Rev.D 88 (2013) 046003 [arXiv:1306.5200] [INSPIRE]. |
| [13] | J.L. Karczmarek and P. Sabella-Garnier, Entanglement entropy on the fuzzy sphere, JHEP03 (2014) 129 [arXiv:1310.8345] [INSPIRE]. · doi:10.1007/JHEP03(2014)129 |
| [14] | P. Sabella-Garnier, Mutual information on the fuzzy sphere, JHEP02 (2015) 063 [arXiv:1409.7069] [INSPIRE]. · doi:10.1007/JHEP02(2015)063 |
| [15] | S. Okuno, M. Suzuki and A. Tsuchiya, Entanglement entropy in scalar field theory on the fuzzy sphere, PTEP2016 (2016) 023B03 [arXiv:1512.06484] [INSPIRE]. · Zbl 1361.81153 |
| [16] | M. Suzuki and A. Tsuchiya, A generalized volume law for entanglement entropy on the fuzzy sphere, PTEP2017 (2017) 043B07 [arXiv:1611.06336] [INSPIRE]. · Zbl 1524.81017 |
| [17] | W. Fischler, A. Kundu and S. Kundu, Holographic entanglement in a noncommutative gauge theory, JHEP01 (2014) 137 [arXiv:1307.2932] [INSPIRE]. · doi:10.1007/JHEP01(2014)137 |
| [18] | J.L. Karczmarek and C. Rabideau, Holographic entanglement entropy in nonlocal theories, JHEP10 (2013) 078 [arXiv:1307.3517] [INSPIRE]. · Zbl 1342.83107 · doi:10.1007/JHEP10(2013)078 |
| [19] | N. Shiba and T. Takayanagi, Volume law for the entanglement entropy in non-local QFTs, JHEP02 (2014) 033 [arXiv:1311.1643] [INSPIRE]. · doi:10.1007/JHEP02(2014)033 |
| [20] | D.-W. Pang, Holographic entanglement entropy of nonlocal field theories, Phys. Rev.D 89 (2014) 126005 [arXiv:1404.5419] [INSPIRE]. |
| [21] | M.R. Mohammadi Mozaffar and A. Mollabashi, Entanglement in Lifshitz-type quantum field theories, JHEP07 (2017) 120 [arXiv:1705.00483] [INSPIRE]. · Zbl 1380.83098 · doi:10.1007/JHEP07(2017)120 |
| [22] | J. Madore, The fuzzy sphere, Class. Quant. Grav.9 (1992) 69 [INSPIRE]. · Zbl 0742.53039 · doi:10.1088/0264-9381/9/1/008 |
| [23] | M.R. Douglas and N.A. Nekrasov, Noncommutative field theory, Rev. Mod. Phys.73 (2001) 977 [hep-th/0106048] [INSPIRE]. · Zbl 1205.81126 · doi:10.1103/RevModPhys.73.977 |
| [24] | D. Dou and B. Ydri, Entanglement entropy on fuzzy spaces, Phys. Rev.D 74 (2006) 044014 [gr-qc/0605003] [INSPIRE]. |
| [25] | M. Srednicki, Entropy and area, Phys. Rev. Lett.71 (1993) 666 [hep-th/9303048] [INSPIRE]. · Zbl 0972.81649 · doi:10.1103/PhysRevLett.71.666 |
| [26] | H. Casini and M. Huerta, Entanglement entropy in free quantum field theory, J. Phys.A 42 (2009) 504007 [arXiv:0905.2562] [INSPIRE]. · Zbl 1186.81017 |
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