Abstract
We consider the scaling behavior of circuit complexity under quantum quench in an a relativistic fermion field theory on a one dimensional spatial lattice. This is done by finding an exactly solvable quench protocol which asymptotes to massive phases at early and late times and crosses a critical point in between. We find a variety of scaling behavior as a function of the quench rate, starting with a saturation for quenches at the lattice scale, a “fast quench scaling” at intermediate rate and a Kibble Zurek scaling at slow rates.
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References
T.W.B. Kibble, Topology of cosmic domains and strings, J. Phys.A 9 (1976) 1387 [INSPIRE].
W.H. Zurek, Cosmological experiments in superfluid helium?, Nature317 (1985) 505 [INSPIRE].
S. Mondal, D. Sen and K. Sengupta, Non-equilibrium dynamics of quantum systems: order parameter evolution, defect generation, and qubit transfer, in Quantum quenching, annealing and computation, Lect. Notes Phys.802, Springer, Berlin Heidelberg, Germany (2010), pg. 21 [arXiv:0908.2922].
V. Gritsev and A. Polkovnikov, Universal dynamics near quantum critical points, in Understanding quantum phase transitions, L.D. Carr ed., Taylor & Francis, Boca Raton, FL, U.S.A. (2010) [arXiv:0910.3692] [INSPIRE].
J. Dziarmaga, Dynamics of a quantum phase transition and relaxation to a steady state, Adv. Phys.59 (2010) 1063 [arXiv:0912.4034].
A. Polkovnikov, K. Sengupta, A. Silva and M. Vengalattore, Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys.83 (2011) 863 [arXiv:1007.5331] [INSPIRE].
A. Lamacraft and J.E. Moore, Potential insights into non-equilibrium behaviour from atomic physics, in Ultracold bosonic and fermionic gases, A. Fletcher, K. Levin and D. Stamper-Kurn eds., Contemp. Concepts Cond. Matter Sci.5, Elsevier, The Netherlands (2012), pg. 177 [arXiv:1106.3567].
A. Chandran, A. Erez, S.S. Gubser and S.L. Sondhi, Kibble-Zurek problem: universality and the scaling limit, Phys. Rev.B 86 (2012) 064304 [arXiv:1202.5277].
S.R. Das, D.A. Galante and R.C. Myers, Universal scaling in fast quantum quenches in conformal field theories, Phys. Rev. Lett.112 (2014) 171601 [arXiv:1401.0560] [INSPIRE].
S.R. Das, D.A. Galante and R.C. Myers, Universality in fast quantum quenches, JHEP02 (2015) 167 [arXiv:1411.7710] [INSPIRE].
S.R. Das, D.A. Galante and R.C. Myers, Smooth and fast versus instantaneous quenches in quantum field theory, JHEP08 (2015) 073 [arXiv:1505.05224] [INSPIRE].
S.R. Das, D.A. Galante and R.C. Myers, Quantum quenches in free field theory: universal scaling at any rate, JHEP05 (2016) 164 [arXiv:1602.08547] [INSPIRE].
D. Das, S.R. Das, D.A. Galante, R.C. Myers and K. Sengupta, An exactly solvable quench protocol for integrable spin models, JHEP11 (2017) 157 [arXiv:1706.02322] [INSPIRE].
A. Dymarsky and M. Smolkin, Universality of fast quenches from the conformal perturbation theory, JHEP01 (2018) 112 [arXiv:1709.08654] [INSPIRE].
M. Goykhman, T. Shachar and M. Smolkin, On fast quenches and spinning correlators, JHEP06 (2018) 168 [arXiv:1804.03855] [INSPIRE].
M. Goykhman, T. Shachar and M. Smolkin, On quantum quenches at one loop, JHEP01 (2019) 022 [arXiv:1810.02258] [INSPIRE].
S.R. Das, Old and new scaling laws in quantum quench, PTEP2016 (2016) 12C107 [arXiv:1608.04407] [INSPIRE].
J. Sonner, A. del Campo and W.H. Zurek, Universal far-from-equilibrium dynamics of a holographic superconductor, arXiv:1406.2329 [INSPIRE].
P.M. Chesler, A.M. Garcia-Garcia and H. Liu, Defect formation beyond Kibble-Zurek mechanism and holography, Phys. Rev.X 5 (2015) 021015 [arXiv:1407.1862] [INSPIRE].
A. Buchel, L. Lehner and R.C. Myers, Thermal quenches in N = 2∗ plasmas, JHEP08 (2012) 049 [arXiv:1206.6785] [INSPIRE].
A. Buchel, L. Lehner, R.C. Myers and A. van Niekerk, Quantum quenches of holographic plasmas, JHEP05 (2013) 067 [arXiv:1302.2924] [INSPIRE].
A. Buchel, R.C. Myers and A. van Niekerk, Universality of abrupt holographic quenches, Phys. Rev. Lett.111 (2013) 201602 [arXiv:1307.4740] [INSPIRE].
P. Caputa, S.R. Das, M. Nozaki and A. Tomiya, Quantum quench and scaling of entanglement entropy, Phys. Lett.B 772 (2017) 53 [arXiv:1702.04359] [INSPIRE].
M. Nishida, M. Nozaki, Y. Sugimoto and A. Tomiya, Entanglement spreading and oscillation, J. Stat. Mech.1905 (2019) 053102 [arXiv:1712.09899] [INSPIRE].
H.A. Camargo, P. Caputa, D. Das, M.P. Heller and R. Jefferson, Complexity as a novel probe of quantum quenches: universal scalings and purifications, Phys. Rev. Lett.122 (2019) 081601 [arXiv:1807.07075] [INSPIRE].
L. Susskind, Computational complexity and black hole horizons, Fortsch. Phys.64 (2016) 24 [Addendum ibid.64 (2016) 44] [arXiv:1403.5695] [arXiv:1402.5674] [INSPIRE].
D. Stanford and L. Susskind, Complexity and shock wave geometries, Phys. Rev.D 90 (2014) 126007 [arXiv:1406.2678] [INSPIRE].
L. Susskind and Y. Zhao, Switchbacks and the bridge to nowhere, arXiv:1408.2823 [INSPIRE].
L. Susskind, Entanglement is not enough, Fortsch. Phys.64 (2016) 49 [arXiv:1411.0690] [INSPIRE].
A.R. Brown, D.A. Roberts, L. Susskind, B. Swingle and Y. Zhao, Holographic complexity equals bulk action?, Phys. Rev. Lett.116 (2016) 191301 [arXiv:1509.07876] [INSPIRE].
A.R. Brown, D.A. Roberts, L. Susskind, B. Swingle and Y. Zhao, Complexity, action and black holes, Phys. Rev.D 93 (2016) 086006 [arXiv:1512.04993] [INSPIRE].
D. Carmi, S. Chapman, H. Marrochio, R.C. Myers and S. Sugishita, On the time dependence of holographic complexity, JHEP11 (2017) 188 [arXiv:1709.10184] [INSPIRE].
S.A. Hosseini Mansoori, V. Jahnke, M.M. Qaemmaqami and Y.D. Olivas, Holographic complexity of anisotropic black branes, arXiv:1808.00067 [INSPIRE].
R. Jefferson and R.C. Myers, Circuit complexity in quantum field theory, JHEP10 (2017) 107 [arXiv:1707.08570] [INSPIRE].
S. Chapman, M.P. Heller, H. Marrochio and F. Pastawski, Toward a definition of complexity for quantum field theory states, Phys. Rev. Lett.120 (2018) 121602 [arXiv:1707.08582] [INSPIRE].
R. Khan, C. Krishnan and S. Sharma, Circuit complexity in fermionic field theory, Phys. Rev.D 98 (2018) 126001 [arXiv:1801.07620] [INSPIRE].
L. Hackl and R.C. Myers, Circuit complexity for free fermions, JHEP07 (2018) 139 [arXiv:1803.10638] [INSPIRE].
M. Guo, J. Hernandez, R.C. Myers and S.-M. Ruan, Circuit complexity for coherent states, JHEP10 (2018) 011 [arXiv:1807.07677] [INSPIRE].
S. Chapman et al., Complexity and entanglement for thermofield double states, SciPost Phys.6 (2019) 034 [arXiv:1810.05151] [INSPIRE].
A. Bhattacharyya, A. Shekar and A. Sinha, Circuit complexity in interacting QFTs and RG flows, JHEP10 (2018) 140 [arXiv:1808.03105] [INSPIRE].
R.-Q. Yang, Y.-S. An, C. Niu, C.-Y. Zhang and K.-Y. Kim, Principles and symmetries of complexity in quantum field theory, Eur. Phys. J.C 79 (2019) 109 [arXiv:1803.01797] [INSPIRE].
R.-Q. Yang, Y.-S. An, C. Niu, C.-Y. Zhang and K.-Y. Kim, More on complexity of operators in quantum field theory, JHEP03 (2019) 161 [arXiv:1809.06678] [INSPIRE].
R.-Q. Yang and K.-Y. Kim, Complexity of operators generated by quantum mechanical Hamiltonians, JHEP03 (2019) 010 [arXiv:1810.09405] [INSPIRE].
P. Caputa, N. Kundu, M. Miyaji, T. Takayanagi and K. Watanabe, Anti-de Sitter space from optimization of path integrals in conformal field theories, Phys. Rev. Lett.119 (2017) 071602 [arXiv:1703.00456] [INSPIRE].
P. Caputa, N. Kundu, M. Miyaji, T. Takayanagi and K. Watanabe, Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT, JHEP11 (2017) 097 [arXiv:1706.07056] [INSPIRE].
A. Bhattacharyya, P. Caputa, S.R. Das, N. Kundu, M. Miyaji and T. Takayanagi, Path-integral complexity for perturbed CFTs, JHEP07 (2018) 086 [arXiv:1804.01999] [INSPIRE].
A.P. Reynolds and S.F. Ross, Complexity of the AdS soliton, Class. Quant. Grav.35 (2018) 095006 [arXiv:1712.03732] [INSPIRE].
K. Hashimoto, N. Iizuka and S. Sugishita, Time evolution of complexity in Abelian gauge theories, Phys. Rev.D 96 (2017) 126001 [arXiv:1707.03840] [INSPIRE].
R.-Q. Yang, C. Niu, C.-Y. Zhang and K.-Y. Kim, Comparison of holographic and field theoretic complexities for time dependent thermofield double states, JHEP02 (2018) 082 [arXiv:1710.00600] [INSPIRE].
K. Hashimoto, N. Iizuka and S. Sugishita, Thoughts on holographic complexity and its basis-dependence, Phys. Rev.D 98 (2018) 046002 [arXiv:1805.04226] [INSPIRE].
J. Jiang and X. Liu, Circuit complexity for fermionic thermofield double states, Phys. Rev.D 99 (2019) 026011 [arXiv:1812.00193] [INSPIRE].
D.W.F. Alves and G. Camilo, Evolution of complexity following a quantum quench in free field theory, JHEP06 (2018) 029 [arXiv:1804.00107] [INSPIRE].
J. Jiang, J. Shan and J. Yang, Circuit complexity for free Fermion with a mass quench, arXiv:1810.00537 [INSPIRE].
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Liu, S. Complexity and scaling in quantum quench in 1 + 1 dimensional fermionic field theories. J. High Energ. Phys. 2019, 104 (2019). https://doi.org/10.1007/JHEP07(2019)104
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DOI: https://doi.org/10.1007/JHEP07(2019)104