Abstract
We globally quench the theory of two dimensional massless fermions (many flavours) with quartic interactions by making the quartic coupling a smooth function of time. Working in a derivative expansion we show that the discrete ℤ2 symmetry in case of the Gross-Neveu model, and the U (1) symmetry in case of the Nambu-Jona-Lasinio2 model, are restored during the zero-temperature quench. For the Gross-Neveu model we show that this can be understood as an effective thermalization. The time of symmetry restoration shows scaling with the quench rate. We identify this with the Kibble-Zurek scaling in the problem. In a suitable double scaling limit, the symmetry restoration may be understood in terms of Liouville quantum mechanics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.R. Das, D.A. Galante and R.C. Myers, Quantum quenches in free field theory: universal scaling at any rate, JHEP 05 (2016) 164 [arXiv:1602.08547] [INSPIRE].
P. Calabrese and J.L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 0504 (2005) P04010 [cond-mat/0503393] [INSPIRE].
S. Sotiriadis and J. Cardy, Quantum quench in interacting field theory: a self-consistent approximation, Phys. Rev. B 81 (2010) 134305 [arXiv:1002.0167] [INSPIRE].
B. Bertini, D. Schuricht and F.H.L. Essler, Quantum quench in the sine-Gordon model, J. Stat. Mech. 10 (2014) P10035.
D. Boyanovsky, D. Cormier, H.J. de Vega and R. Holman, Out-of-equilibrium dynamics of an inflationary phase transition, Phys. Rev. D 55 (1997) 3373 [hep-ph/9610396] [INSPIRE].
D. Boyanovsky, D. Cormier, H.J. de Vega, R. Holman, A. Singh and M. Srednicki, Scalar field dynamics in Friedman-Robertson-Walker space-times, Phys. Rev. D 56 (1997) 1939 [hep-ph/9703327] [INSPIRE].
E. Shuryak, Physics of strongly coupled quark-gluon plasma, Prog. Part. Nucl. Phys. 62 (2009) 48 [arXiv:0807.3033] [INSPIRE].
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/string duality, hot QCD and heavy ion collisions, Cambridge University Press, Cambridge U.K. (2014), arXiv:1101.0618 [INSPIRE].
D.A. Galante, Universal scaling properties after quantum quenches, Ph.D. thesis, Western Ontario University, U.S.A. (2016).
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?, Nature 317 (1985) 505 [INSPIRE].
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].
S.R. Das, Old and new scaling laws in quantum quench, PTEP 2016 (2016) 12C107 [arXiv:1608.04407] [INSPIRE].
S.R. Das, D.A. Galante and R.C. Myers, Universality in fast quantum quenches, JHEP 02 (2015) 167 [arXiv:1411.7710] [INSPIRE].
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, Smooth and fast versus instantaneous quenches in quantum field theory, JHEP 08 (2015) 073 [arXiv:1505.05224] [INSPIRE].
S. Mondal, D. Sen and K. Sengupta, Non-equilibrium dynamics of quantum systems: order parameter evolution, defect generation, and qubit transfer, Lect. Notes Phys. 802 (2010) 21 [arXiv:0908.2922].
U. Divakaran, V. Mukherjee, A. Dutta and D. Sen, Defect production due to quenching through a multicritical point and along a gapless line, Springer, Berlin Germany (2010).
D. Das, S.R. Das, D.A. Galante, R.C. Myers and K. Sengupta, An exactly solvable quench protocol for integrable spin models, JHEP 11 (2017) 157 [arXiv:1706.02322] [INSPIRE].
M. Goykhman, T. Shachar and M. Smolkin, On quantum quenches at one loop, JHEP 01 (2019) 022 [arXiv:1810.02258] [INSPIRE].
S.R. Das and K. Sengupta, Non-equilibrium dynamics of O(N ) nonlinear σ-models: a large-N approach, JHEP 09 (2012) 072 [arXiv:1202.2458] [INSPIRE].
S. Gemsheim, I. Mandal, K. Sengupta and Z. Wang, Order parameter dynamics of the non-linear σ-model in the large N limit, Eur. Phys. J. B 93 (2020) 40 [arXiv:1906.05306] [INSPIRE].
L. Jacobs, Critical behavior in a class of O(n) invariant field theories in two-dimensions, Phys. Rev. D 10 (1974) 3956 [INSPIRE].
B.J. Harrington and A. Yildiz, Restoration of dynamically broken symmetries at finite temperature, Phys. Rev. D 11 (1975) 779 [INSPIRE].
D.J. Gross and A. Neveu, Dynamical symmetry breaking in asymptotically free field theories, Phys. Rev. D 10 (1974) 3235 [INSPIRE].
I.L. Buchbinder and E.N. Kirillova, Gross-Neveu model in curved space-time: the effective potential and curvature induced phase transition, Int. J. Mod. Phys. A 4 (1989) 143 [INSPIRE].
A. Kamenev and A. Levchenko, Keldysh technique and non-linear sigma-model: basic principles and applications, Adv. Phys. 58 (2009) 197.
A. Ferreiro and J. Navarro-Salas, Pair creation in electric fields, anomalies and renormalization of the electric current, Phys. Rev. D 97 (2018) 125012 [arXiv:1803.03247] [INSPIRE].
S. Sachdev, Quantum phase transitions, 2nd edition, Cambridge University Press, Cambridge U.K. (2011).
P.H. Ginsparg and G.W. Moore, Lectures on 2 − D gravity and 2 − D string theory, in the proceedings of Theoretical Advanced Study Institute (TASI 92): From Black Holes and Strings to Particles, June 1–16, Boulder U.S.A. (1992), hep-th/9304011 [INSPIRE].
D. Bagrets, A. Altland and A. Kamenev, Sachdev-Ye-Kitaev model as Liouville quantum mechanics, Nucl. Phys. B 911 (2016) 191 [arXiv:1607.00694] [INSPIRE].
Z.-H. Yang and Y.-M. Chu, On approximating the modified Bessel function of the second kind, J. Ineq. Applicat. 2017 (2017) 41.
A. Eberlein, V. Kasper, S. Sachdev and J. Steinberg, Quantum quench of the Sachdev-Ye-Kitaev model, Phys. Rev. B 96 (2017) 205123 [arXiv:1706.07803] [INSPIRE].
M.J. Bhaseen, J.P. Gauntlett, B.D. Simons, J. Sonner and T. Wiseman, Holographic superfluids and the dynamics of symmetry breaking, Phys. Rev. Lett. 110 (2013) 015301 [arXiv:1207.4194] [INSPIRE].
A.C. Petkou and G. Siopsis, M-theory and the Gross-Neveu model in 2 + 1 dimensions, Phys. Lett. B 640 (2006) 209 [hep-th/0509143] [INSPIRE].
P. Hořava and C.A. Keeler, Noncritical M-theory in 2 + 1 dimensions as a nonrelativistic Fermi liquid, JHEP 07 (2007) 059 [hep-th/0508024] [INSPIRE].
M. Kolodrubetz, E. Katz and A. Polkovnikov, Dynamic trapping near a quantum critical point, Phys. Rev. B 91 (2015) 054306 [arXiv:1406.2701] [INSPIRE].
L. Kofman, A. Linde, X. Liu, A. Maloney, L. McAllister and E. Silverstein, Beauty is attractive: moduli trapping at enhanced symmetry points, JHEP 05 (2004) 030.
L. D’Alessio, Y. Kafri, A. Polkovnikov and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65 (2016) 239 [arXiv:1509.06411] [INSPIRE].
T. Mori and N. Shiraishi, Thermalization without eigenstate thermalization hypothesis after a quantum quench, Phys. Rev. E 96 (2017) 022153 [arXiv:1707.05921] [INSPIRE].
E. Antonyan, J.A. Harvey and D. Kutasov, The Gross-Neveu model from string theory, Nucl. Phys. B 776 (2007) 93 [hep-th/0608149] [INSPIRE].
A. Basu and A. Maharana, Generalized Gross-Neveu models and chiral symmetry breaking from string theory, Phys. Rev. D 75 (2007) 065005 [hep-th/0610087] [INSPIRE].
A.I. Larkin and Y.N. Ovchinnikov, Quasiclassical method in the theory of superconductivity, Sov. J. Exp. Theor. Phys. 28 (1969) 1200.
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
K. Hashimoto, K. Murata and K. Yoshida, Chaos in chiral condensates in gauge theories, Phys. Rev. Lett. 117 (2016) 231602 [arXiv:1605.08124] [INSPIRE].
U. Wolff, The phase diagram of the infinite N Gross-Neveu model at finite temperature and chemical potential, Phys. Lett. B 157 (1985) 303 [INSPIRE].
G. Basar and G.V. Dunne, Gross-Neveu models, nonlinear Dirac equations, surfaces and strings, JHEP 01 (2011) 127 [arXiv:1011.3835] [INSPIRE].
Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. 1., Phys. Rev. 122 (1961) 345 [INSPIRE].
D. Grosser, Parity violation, compositeness, and the Gross-Neveu model, J. Phys. G 11 (1985) 9 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2003.11745
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Das, D., Dey, B. Quantum quench, large N, and symmetry restoration. J. High Energ. Phys. 2020, 107 (2020). https://doi.org/10.1007/JHEP07(2020)107
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2020)107