- Letter
- Open Access
Anomalous universal adiabatic dynamics: The case of the Fredkin model
Phys. Rev. Research 5, L012048 – Published 27 March, 2023
DOI: https://doi.org/10.1103/PhysRevResearch.5.L012048
Abstract
When a system is driven across a second-order quantum phase transition, the number of defects which are produced scales with the speed of the variation of the tuning parameter according to a universal law described by the Kibble-Zurek mechanism. We study a possible breakdown of this prediction proving that the number of defects can exhibit another universal scaling law which is still related only to the critical exponents and , but differs from the Kibble-Zurek result. Finally, we provide an example, the deformed Fredkin spin chain, where this violation of the standard adiabatic dynamics can occur.
Physics Subject Headings (PhySH)
Article Text
References (21)
- S. Sachdev, Quantum Phase Transition (Cambridge University Press, Cambridge, 1999).
- W. H. Zurek, U. Dorner, and P. Zoller, Dynamics of a Quantum Phase Transition, Phys. Rev. Lett. 95, 105701 (2005).
- J. Dziarmaga, Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model, Phys. Rev. Lett. 95, 245701 (2005).
- A. Polkovnikov, Universal adiabatic dynamics in the vicinity of a quantum critical point, Phys. Rev. B 72, 161201(R) (2005).
- T. W. B. Kibble, Topology of cosmic domains and strings, J. Phys. A: Math. Gen. 9, 1387 (1976).
- W. H. Zurek, Cosmological experiments in superfluid helium? Nature (London) 317, 505 (1985).
- A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83, 863 (2011).
- A. del Campo and W. H. Zurek, Universality of phase transition dynamics: Topological defects from symmetry breaking, Int. J. Mod. Phys. A 29, 1430018 (2014).
- O. Salberger, T. Udagawa, Z. Zhang, H. Katsura, I. Klich, and V. Korepin, Deformed Fredkin spin chain with extensive entanglement, J. Stat. Mech. (2017) 063103.
- J. K. Pachos and E. Rico, Effective three-body interactions in triangular optical lattices, Phys. Rev. A 70, 053620 (2004).
- L. Dell'Anna, O. Salberger, L. Barbiero, A. Trombettoni, and V. E. Korepin, Violation of cluster decomposition and absence of light cones in local integer and half-integer spin chains, Phys. Rev. B 94, 155140 (2016).
- O. Salberger and V. Korepin, Entangled spin chain, Rev. Math. Phys. 29, 1750031 (2017).
- C. Domb, M. Green, and J. Lebowitz, Phase Transitions and Critical Phenomena (Academic Press, New York, 1983), Vol. 8.
- X. Chen, E. Fradkin, and W. Witczak-Krempa, Gapless quantum spin chains: Multiple dynamics and conformal wavefunctions, J. Phys. A: Math. Theor. 50, 464002 (2017).
- T. W. Burkhardt and I. Guim, Finite-size scaling of the quantum Ising chain with periodic, free, and antiperiodic boundary conditions, J. Phys. A: Math. Gen. 18, L33 (1985).
- U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. 326, 96 (2011).
- N. Defenu, G. Morigi, L. Dell'Anna, and T. Enss, Universal dynamical scaling of long-range topological superconductors, Phys. Rev. B 100, 184306 (2019).
- G. Francica and L. Dell'Anna, Correlations, long-range entanglement and dynamics in long-range Kitaev chains, Phys. Rev. B 106, 155126 (2022).
- G. Roósz, U. Divakaran, H. Rieger, and F. Iglói, Nonequilibrium quantum relaxation across a localization-delocalization transition, Phys. Rev. B 90, 184202 (2014).
- A. Dutta, A. Rahmani, and A. del Campo, Anti-Kibble-Zurek Behavior in Crossing the Quantum Critical Point of a Thermally Isolated System Driven by a Noisy Control Field, Phys. Rev. Lett. 117, 080402 (2016).
- H.-B. Zeng, C.-Y. Xia, and A. del Campo, Universal Breakdown of Kibble-Zurek Scaling in Fast Quenches Across a Phase Transition, Phys. Rev. Lett. 130, 060402 (2023).