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Breakdown of the adiabatic limit in low-dimensional gapless systems

Nature Physics volume 4, pages 477–481 (2008)Cite this article

Abstract

It is generally believed that a generic system can be reversibly transformed from one state to another by a sufficiently slow change of parameters. Microscopically, this belief is often justified using connections to the quantum adiabatic theorem stating that there are no transitions between different energy levels if the hamiltonian changes slowly in time. Here, we show that in fact the response to such a slow change can be non-trivial in low-dimensional gapless systems. We identify three generic regimes of the response: analytic, non-analytic and non-adiabatic, which are characterized by a different behaviour of the heating induced in the system with the ramp rate. In the last regime, the limits of the ramp rate going to zero and the system size going to infinity do not commute and the adiabatic process does not exist in the thermodynamic limit. We support our results with numerical and analytical calculations.

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Figure 1: Dependence of the energy density added to a one-dimensional system of linear size L=128 during the ramp on the parameter δ for different initial temperatures.
Figure 2: Dependence of on δ for different sizes at fixed temperature T=0.02.
Figure 3: Dependence of on δ in a two-dimensional system for two different sizes.
Figure 4: Correlation function 〈ai†ai+j〉 as a function of scaled distance L/πsin(πj/L) at different moments of time.

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References

  1. Landau, L. D. & Lifshitz, E. M. Statistical Physics 1 (Butterworth-Heinemann, Oxford, 1999).

    Google Scholar 

  2. Balian, R. From Microphysics to Macrophysics (Springer, Berlin, 1991).

    Book  Google Scholar 

  3. Sachdev, S. Quantum Phase Transitions (Cambridge Univ. Press, Cambridge, 1999).

    MATH  Google Scholar 

  4. Chaikin, P. M. & Lubensky, T. C. Principles of Condensed Matter Physics (Cambridge Univ. Press, Cambridge, 1995).

    Book  Google Scholar 

  5. Dobrescu, B. E. & Pokrovsky, V. L. Production efficiency of Feshbach molecules in fermion systems. Phys. Lett. A 350, 154–158 (2006).

    Article  ADS  Google Scholar 

  6. Altland, A. & Gurarie, V. Many body generalization of the Landau Zener problem. Phys. Rev. Lett. 100, 063602 (2008).

    Article  ADS  Google Scholar 

  7. Strecker, K. E., Partridge, G. B. & Hulet, R. G. Conversion of an atomic Fermi gas to a long-lived molecular Bose gas. Phys. Rev. Lett. 91, 080406 (2003).

    Article  ADS  Google Scholar 

  8. Polkovnikov, A. Universal adiabatic dynamics in the vicinity of a quantum critical point. Phys. Rev. B 72, 161201(R) (2005).

    Article  ADS  Google Scholar 

  9. Zurek, W. H., Dorner, U. & Zoller, P. Dynamics of a quantum phase transition. Phys. Rev. Lett. 95, 105701 (2005).

    Article  ADS  Google Scholar 

  10. Dziarmaga, J. Dynamics of a quantum phase transition: Exact solution of the quantum Ising model. Phys. Rev. Lett. 95, 245701 (2005).

    Article  ADS  Google Scholar 

  11. Fubini, A., Falci, G. & Osterloh, A. Robustness of adiabatic passage through a quantum phase transition. New J. Phys. 9, 134 (2007).

    Article  ADS  Google Scholar 

  12. Dziarmaga, J. Dynamics of a quantum phase transition in the random Ising model: Logarithmic dependence of the defect density on the transition rate. Phys. Rev. B 74, 064416 (2006).

    Article  ADS  Google Scholar 

  13. Caneva, T., Fazio, R. & Santoro, G. E. Adiabatic quantum dynamics of a random Ising chain across its quantum critical point. Phys. Rev. B 76, 174303 (2007).

    Article  Google Scholar 

  14. Mukherjee, V., Divakaran, U., Dutta, A. & Sen, D. Quenching dynamics of a quantum XY spin-1/2 chain in a transverse field. Phys. Rev. B 76, 174303 (2007).

    Article  ADS  Google Scholar 

  15. Zurek, W. H. Cosmological experiments in condensed matter systems. Phys. Rep. 276, 177–221 (1996).

    Article  ADS  Google Scholar 

  16. Farhi, E. et al. A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292, 472–476 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  17. Vilenkin, A. Many Worlds in One: The Search for Other Universes (Hill and Wang, New York, 2006).

    MATH  Google Scholar 

  18. Parker, L. Quantized fields and particle creation in expanding universes. I. Phys. Rev. 183, 1057–1068 (1969); II. Phys. Rev. D 3, 346–356 (1971).

  19. Danielsson, U. H. Lectures on string theory and cosmology. Class. Quant. Grav. 22, S1–S39 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  20. Polkovnikov, A. Quantum corrections to the dynamics of interacting bosons: Beyond the truncated Wigner approximation. Phys. Rev. A 68, 053604 (2003).

    Article  ADS  Google Scholar 

  21. Polkovnikov, A., Sachdev, S. & Girvin, S. M. Nonequilibrium Gross–Pitaevskii dynamics of boson lattice models. Phys. Rev. A 66, 053607 (2002).

    Article  ADS  Google Scholar 

  22. Bloch, I., Dalibard, J. & Zwerger, W. Rev. Mod. Phys.; Preprint at <http://arXiv:0704.3011> (2008) Many-body physics with ultracold gases.

Download references

Acknowledgements

We would like to acknowledge E. Altman, E. Demler, A. Garkun, S. Girvin, V. Gurarie, M. Lukin, V. Pokrovsky and N. Prokof’ev for useful discussions. A.P. was supported by AFOSR YIP and partially by NSF under grant PHY05-51164. V.G. is partially supported by the Swiss National Science Foundation and AFOSR. A.P. also acknowledges the Kavli Institute for Theoretical Physics for hospitality.

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  1. Department of Physics, Boston University, Boston, Massachusetts 02215, USA

    Anatoli Polkovnikov

  2. Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

    Vladimir Gritsev

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  1. Anatoli Polkovnikov
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  2. Vladimir Gritsev
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The authors have made equal contributions in preparing and writing this work.

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Correspondence to Anatoli Polkovnikov.

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Polkovnikov, A., Gritsev, V. Breakdown of the adiabatic limit in low-dimensional gapless systems. Nature Phys 4, 477–481 (2008). https://doi.org/10.1038/nphys963

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