Emergent Holographic Forces from Tensor Networks and Criticality (2401.13595v1)
Abstract: The AdS/CFT correspondence stipulates a duality between conformal field theories and certain theories of quantum gravity in one higher spatial dimension. However, probing this conjecture on contemporary classical or quantum computers is challenging. We formulate an efficiently implementable multi-scale entanglement renormalization ansatz (MERA) model of AdS/CFT providing a mapping between a (1+1)-dimensional critical spin system and a (2+1)-dimensional bulk theory. Using a combination of numerics and analytics, we show that the bulk theory arising from this optimized tensor network furnishes excitations with attractive interactions. Remarkably, these excitations have one- and two-particle energies matching the predictions for matter coupled to AdS gravity at long distances, thus displaying key features of AdS physics. We show that these potentials arise as a direct consequence of entanglement renormalization and discuss how this approach can be used to efficiently simulate bulk dynamics using realistic quantum devices.
- G. Hooft, gr-qc/9310026 (1993).
- L. Susskind, Journal of Mathematical Physics 36, 6377 (1995).
- J. Maldacena, International Journal of Theoretical Physics 38, 1113 (1999).
- E. Witten, hep-th/9802150 (1998).
- L. Susskind and E. Witten, hep-th/9805114 (1998).
- S. Sachdev and J. Ye, Physical Review Letters 70, 3339 (1993).
- A. Kitaev, KITP strings seminar and Entanglement 2015 program (2015).
- J. Maldacena and D. Stanford, Physical Review D 94, 106002 (2016).
- J. Maldacena, arXiv:2303.11534 (2023).
- A. M. García-García, C. Liu, and J. J. M. Verbaarschot, “Sparsity independent Lyapunov exponent in the Sachdev-Ye-Kitaev model,” (2023), arXiv:2311.00639 [hep-th] .
- X.-L. Qi, “Exact holographic mapping and emergent space-time geometry,” (2013), arXiv:1309.6282 [hep-th] .
- G. Vidal, Phys. Rev. Lett. 101, 110501 (2008).
- G. Vidal, Phys. Rev. Lett. 99, 220405 (2007).
- B. Swingle, arXiv:1209.3304 (2012).
- See supplementary material .
- G. Evenbly and S. R. White, Phys. Rev. Lett. 116, 140403 (2016).
- G. Evenbly and G. Vidal, “Quantum criticality with the multi-scale entanglement renormalization ansatz,” in Strongly Correlated Systems: Numerical Methods, edited by A. Avella and F. Mancini (Springer Berlin Heidelberg, Berlin, Heidelberg, 2013) pp. 99–130.
- G. Evenbly, Phys. Rev. Lett. 119, 141602 (2017), arXiv:1704.04229 [quant-ph] .
- A. Milsted and G. Vidal, (2018), arXiv:1812.00529 [hep-th] .
- R. Haghshenas, E. Chertkov, M. DeCross, T. M. Gatterman, J. A. Gerber, K. Gilmore, D. Gresh, N. Hewitt, C. V. Horst, M. Matheny, T. Mengle, B. Neyenhuis, D. Hayes, and M. Foss-Feig, “Probing critical states of matter on a digital quantum computer,” (2023), arXiv:2305.01650 [quant-ph] .
- R. Sahay, A. Vishwanath, and R. Verresen, “Quantum Spin Puddles and Lakes: NISQ-Era Spin Liquids from Non-Equilibrium Dynamics,” (2023), arXiv:2211.01381 [cond-mat.str-el] .
- L. Tagliacozzo and G. Vidal, Phys. Rev. B 83, 115127 (2011).
- I. Cong, N. Maskara, M. C. Tran, H. Pichler, G. Semeghini, S. F. Yelin, S. Choi, and M. D. Lukin, “Enhancing detection of topological order by local error correction,” (2023), arXiv:2209.12428 [quant-ph] .
- L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999), arXiv:hep-th/9906064 .
- Y. Kusuki and M. Miyaji, Phys. Rev. Lett. 124, 061601 (2020).
- L. Susskind, arXiv:1802.01198 (2018).
- I. H. Kim and M. J. Kastoryano, Journal of High Energy Physics 2017, 1 (2017).
- I. H. Kim and B. Swingle, arXiv:1711.07500 (2017).
- J. Kaplan, “Lectures on AdS/CFT from the bottom up,” (2016).
- J. Cotler and K. Jensen, JHEP 04, 033 (2021), arXiv:2006.08648 [hep-th] .
- J. Cotler and K. Jensen, JHEP 02, 079 (2019), arXiv:1808.03263 [hep-th] .
- A. Milsted and G. Vidal, Phys. Rev. B 96, 245105 (2017).