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The dynamics of quantum criticality revealed by quantum Monte Carlo and holography

Nature Physics volume 10, pages 361–366 (2014)Cite this article

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Abstract

Understanding the dynamics of quantum systems without long-lived excitations (quasiparticles) constitutes an important yet challenging problem. Although numerical techniques can yield results for the dynamics in imaginary time, their reliable continuation to real time has proved difficult. We tackle this issue using the superfluid–insulator quantum critical point of bosons on a two-dimensional lattice, where quantum fluctuations destroy quasiparticles. We present quantum Monte Carlo simulations for two separate lattice realizations. Their low-frequency conductivities turn out to have the same universal dependence on imaginary frequency and temperature. Using the structure of the real-time dynamics of conformal field theories described by the holographic gauge/gravity duality, we then make progress on the problem of analytically continuing the numerical data to real time. Our method yields quantitative and experimentally testable results on the frequency-dependent conductivity near the quantum critical point. Extensions to other observables and universality classes are discussed.

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Figure 1: Probing quantum critical dynamics.
Figure 2: Quantum Monte Carlo data.
Figure 3: Holographic spacetime, which is asymptotically AdS and contains a planar black hole.
Figure 4: Holographic continuation.
Figure 5: Spectrum of quasinormal charge excitations of the superfluid-insulator QCP.
Figure 6: Quantum critical behaviour of the quantum rotor model.

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Acknowledgements

We are grateful to R. Myers and S-S. Lee for answering our questions and making many useful suggestions. We further acknowledge insightful discussions with J. Bhaseen, J. Carrasquilla, K. Chen, D. Chowdhury, A.G. Green, J. McGreevy, L. Pollet, N. Prokof’ev, S. Raju, A. Singh and J. Sonner. While the present paper was being completed we learned of ref. 39, which we have found helpful in improving the accuracy of some of our numerical results. E.S.S. acknowledges allocation of computing time at the Shared Hierarchical Academic Research Computing Network (SHARCNET:www.sharcnet.ca) and support by NSERC. S.S. was supported by the NSF under Grant DMR-1103860 and by the Templeton Foundation. This research was supported in part by Perimeter Institute for Theoretical Physics (W.W-K. and S.S.). Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.

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Authors and Affiliations

  1. Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada

    William Witczak-Krempa

  2. Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada

    Erik S. Sørensen

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

    Subir Sachdev

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E.S.S. performed the large-scale simulations. All authors contributed equally to the analysis of the data and writing of the manuscript.

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Correspondence to William Witczak-Krempa.

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Witczak-Krempa, W., Sørensen, E. & Sachdev, S. The dynamics of quantum criticality revealed by quantum Monte Carlo and holography. Nature Phys 10, 361–366 (2014). https://doi.org/10.1038/nphys2913

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