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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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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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