Journal of Holography Applications in Physics

Analytic Continuation and Temporal Entanglement in Relativistic QFTs Emerging from Quantum Many-Body Systems

Document Type : Regular article

Author

Department of Physics, College of Education, University of Sulaimani, Sulaimani, Kurdistan Region, IRAQ

Abstract

We reinterpret the recent prescription for temporal entanglement entropy via analytic continuation in holographic quantum field theories from the vantage point of emergent relativistic quantum field theories (QFTs) arising from quantum many-body systems. By framing this analytic continuation in terms of tensor network constructions and saddle point structures in holography, we identify the operational underpinnings that connect non-relativistic microscopic models to low-energy temporal entanglement phenomena. We provide a physical justification for complex extremal surfaces and elaborate on the non-commutativity of analytic continuation and saddle selection, supporting these insights with analogies to quantum spin chains and Gaussian states. Our analysis reveals that the geometrization of time in strongly correlated many-body systems is not merely formal but possesses physically interpretable manifestations rooted in UV/IR correspondence and tensor network dualities.

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[1] T. Nishioka, S. Ryu and T. Takayanagi, “Holographic entanglement entropy: an overview”, J. Phys. A 42, 504008 (2009) DOI:10.1088/1751-8113/42/50/504008.
[2] P. Calabrese, F. H. L. Essler and G. Mussardo, “Introduction to ’Quantum Integrability in Out of Equilibrium Systems”, J. Stat. Mech. 064001 (2016) DOI:10.1088/1742- 5468/2016/06/064001.
[3] J. Eisert, M. Cramer and M. B. Plenio, “Colloquium: Area laws for the entanglement entropy”, Rev. Mod. Phys. 82, 277 (2010) DOI:10.1103/RevModPhys.82.277.
[4] M. Heller, F. Ori and A. Serantes, “Temporal Entanglement from Holographic Entanglement Entropy”, [arXiv:2507.17847] (2025).
[5] G. Vidal, “Class of quantum many-body states that can be effciently simulated”, Phys. Rev. Lett. 101, 110501 (2008) DOI:10.1103/PhysRevLett.101.110501.
[6] M. C. Bañuls et al., “Matrix product states for dynamical simulation of infinite chains”, Phys. Rev. Lett. 102, 240603 (2009) DOI:10.1103/PhysRevLett.102.240603.
[7] J. Haegeman et al., “Time-dependent variational principle for quantum lattices”, Phys. Rev. Lett. 107, 070601 (2011) DOI:10.1103/PhysRevLett.107.070601.
[8] M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information”, Cambridge University Press (2000) DOI:10.1017/CBO9780511976667.
[9] B. Swingle, “Entanglement renormalization and holography”, Phys. Rev. D 86, 065007 (2012) DOI:10.1103/PhysRevD.86.065007.
[10] G. Evenbly and G. Vidal, “Tensor network renormalization yields the multiscale entanglement renormalization ansatz”, Phys. Rev. Lett. 115, 180405 (2015) DOI:10.1103/PhysRevLett.115.180405.
[11] S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT”, Phys. Rev. Lett. 96, 181602 (2006) DOI:10.1103/PhysRevLett.96.181602.
[12] G. Guralnik and Z. Guralnik, “Complexified path integrals and the phases of quantum field theory”, Annals of Phys. 325, 2486 (2010) DOI:10.1016/j.aop.2010.05.004.
[13] I. Peschel, “Calculation of reduced density matrices from correlation functions”, J. Phys. A 36, L205 (2003) DOI:10.1088/0305-4470/36/14/101.
[14] G. Vidal, “Effcient classical simulation of slightly entangled quantum computations”, Phys. Rev. Lett. 91, 147902 (2003) DOI:10.1103/PhysRevLett.91.147902.
[15] R. Jefferson and R. C. Myers, “Circuit complexity in quantum field theory”, JHEP 10, 107 (2017) DOI:10.1007/JHEP10(2017)107.
[16] A. Nahum, J. Ruhman, S. Vijay and J. Haah, “Quantum entanglement growth under random unitary dynamics”, Phys. Rev. X 7, 031016 (2017) DOI:10.1103/PhysRevX.7.031016.
[17] A. Elben et al., “Rényi entropies from random quenches in atomic Hubbard and spin models”, Phys. Rev. Lett. 120, 050406 (2018) DOI:10.1103/PhysRevLett.120.050406.
[18] E. Witten, “Analytic Continuation Of Chern-Simons Theory”, AMS/IP Stud. Adv. Math. 50, 347 (2011) DOI:10.1090/amsip/050/16.
[19] M. Kontsevich and Y. Soibelman, “Stability structures, motivic Donaldson-Thomas invariants and cluster transformations”, [arXiv:0811.2435] (2008).
[20] L. Susskind and E. Witten, “The Holographic Bound in Anti-de Sitter Space”, [arXiv:hep-th/9805114] (1998).
[21] A. W. Peet, “TASI lectures on black holes in string theory”, [arXiv:hep-th/0008241] (2000).
[22] Y. Chen and G. Vidal, “Entanglement contour”, J. Stat. Mech. P10011 (2014) DOI:10.1088/1742-5468/2014/10/P10011. 
Journal of Holography Applications in Physics
Volume 5, Issue 3
September 2025
Pages 107-121
  • Receive Date: 29 July 2025
  • Revise Date: 01 September 2025
  • Accept Date: 02 September 2025