Advertisement

Large Scale Numerics Uncovering New States of Matter

  • A. Moreno
  • J. M. P. Carmelo
  • A. Muramatsu
Conference paper

Abstract

While in condensed matter systems the constituents are well known, namely electrons, neutrons and protons, their interplay may give rise to unexpected states of matter. In this contribution we concentrate on strongly correlated electrons in one dimension driven out of equilibrium. This requires in principle, the solution of Schrödinger’s equation dealing with a space of states, whose dimension increases exponentially with the number of electrons. Implementing an algorithm that requires only polynomially increasing computational resources, namely the time-dependent density matrix renormalization group (t-DMRG), we show that an electron injected into the system, fractionalizes in several portions, some of them carrying charge but no spin, and others carrying the spin and partial charge, in spite of the electron being an elementary particle in isolation. The characterization of such a fractionalization of charge and spin was made possible by the access to HPC plattforms with large memory processors.

Notes

Acknowledgements

A. M. and A. M. acknowledge support by the DFG through SFB/TRR 21. A. M. and J. M. P. C. thank the hospitality and support of the Beijing Computational Science Research Center, where part of the work was done. J. M. P. C. thanks the hospitality of the Institut für Theoretische Physik III, Universität Stuttgart, and the financial support by the Portuguese FCT both in the framework of the Strategic Project PEST-C/FIS/UI607/2011 and under SFRH/BSAB/1177/2011, the German transregional collaborative research center SFB/TRR21, and Max Planck Institute for Solid State Research. A. M. thanks the KITP, Santa Barbara, for hospitality. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. We are very grateful to HLRS (Stuttgart) and NIC (Jülich) for providing the necessary supercomputer resources.

References

  1. 1.
    Balibar, S.: The enigma of supersolidity. Nature 464 pp. 176–182, (2010)CrossRefGoogle Scholar
  2. 2.
    Mazin, I.: Superconductivity gets an iron boost. Nature 464 pp. 183–186, (2010)CrossRefGoogle Scholar
  3. 3.
    Stern, A.: Non-Abelian states of matter. Nature 464 pp. 187–193, (2010)CrossRefGoogle Scholar
  4. 4.
    Moore, C.: The birth of topological insulators. Nature 464 pp. 194–198, (2010)CrossRefGoogle Scholar
  5. 5.
    Balents, L.: Spin liquids in frustrated magnets. Nature 464 pp. 199–208, (2010)CrossRefGoogle Scholar
  6. 6.
    Deshpande, V. V., Bockrath, M., Glazman, L. I., and Yacoby, A.: Electron liquids and solids in one dimension. Nature 464 pp. 209–216, (2010)CrossRefGoogle Scholar
  7. 7.
    Csontos, D.: Exotic matter. Nature 464 pp. 175, (2010)CrossRefGoogle Scholar
  8. 8.
    T. Giamarchi, Quantum Physics in One Dimension (Clarendon Press, Oxford, 2004).MATHGoogle Scholar
  9. 9.
    T. Lorenz, M. Hofmann, M. Gruninger, A. Freimuth, G. S. Uhrig, M. Dumm, and M. Dressel, Nature 418, 614 (2002).CrossRefGoogle Scholar
  10. 10.
    O. M. Auslaender, H. Steinberg, A. Yacoby, Y. Tserkovnyak, B. I. Halperin, K. W. Baldwin, L. N. Pfeiffer, and K. W. West, Science 308, 88 (2005).CrossRefGoogle Scholar
  11. 11.
    C. Blumenstein, J. Schäfer, S. Mietke, A. Dollinger, M. Lochner, X. Y. Cui, L. Patthey, R. Matzdorf, and R. Claessen, Nature Phys. 7, 776 (2011).CrossRefGoogle Scholar
  12. 12.
    K.-V. Pham, M. Gabay, and P. Lederer, Phys. Rev. B 61, 16397 (2000).CrossRefGoogle Scholar
  13. 13.
    H. Steinberg, G. Barak, A. Yacoby, L. N. Pfeiffer, K. W. West, B. I. Halperin, and K. L. Hur, Nature Phys. 4, 116 (2008).CrossRefGoogle Scholar
  14. 14.
    A. Imambekov and L. I. Glazman, Science 323, 228 (2009).MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    A. Shashi, L. I. Glazman, J.-S. Caux, and A. Imambekov, Phys. Rev. B 84, 045408 (2011).CrossRefGoogle Scholar
  16. 16.
    J. M. P. Carmelo, K. Penc, and D. Bozi, Nucl. Phys. B 725, 421 (2005); 737, 351 (2006).Google Scholar
  17. 17.
    G. Barak, H. Steinberg, L. N. Pfeiffer, K. W. West, L. Glazman, F. von Oppen, and A. Yacoby, Nature Phys. 6, 489 (2010).CrossRefGoogle Scholar
  18. 18.
    A. Moreno, A. Muramatsu, and J. M. P. Carmelo, Phys. Rev. B 87, 075101 (2013).CrossRefGoogle Scholar
  19. 19.
    S. R. White and A. E. Feiguin, Phys. Rev. Lett 93, 076401 (2004).CrossRefGoogle Scholar
  20. 20.
    A. J. Daley, C. Kollath, U. Schollwöck, and G. Vidal, J. Stat. Mech.: Theor. Exp. P04005 (2004).Google Scholar
  21. 21.
    P. A. Bares, G. Blatter, and M. Ogata, Phys. Rev. B 44, 130 (1991).CrossRefGoogle Scholar
  22. 22.
    P. A. Bares, J. M. P. Carmelo, J. Ferrer, and P. Horsch, Phys. Rev. B 46, 14624 (1992).CrossRefGoogle Scholar
  23. 23.
    M. Ogata, M. Luchini, S. Sorella, and F. Assaad, Phys. Rev. Lett 66, 2388 (1991).CrossRefGoogle Scholar
  24. 24.
    A. Moreno, A. Muramatsu, and S. R. Manmana, Phys. Rev. B 83, 205113 (2011).CrossRefGoogle Scholar
  25. 25.
    S. R. White, Phys. Rev. Lett 69, 2863 (1992).CrossRefGoogle Scholar
  26. 26.
    S. R. White, Phys. Rev. B 48, 10345 (1993).CrossRefGoogle Scholar
  27. 27.
    U. Schollwöck, Rev. Mod. Phys. 77, 259 (2005).CrossRefGoogle Scholar
  28. 28.
    U. Schollwöck, Ann. Phys. 326, 96 (2011).CrossRefMATHGoogle Scholar
  29. 29.
    J. M. P. Carmelo, L. M. Martelo, and K. Penc, Nucl. Phys. B 737, 237 (2006).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • A. Moreno
    • 1
  • J. M. P. Carmelo
    • 1
    • 2
    • 3
  • A. Muramatsu
    • 1
    • 3
  1. 1.Institut für Theoretische Physik IIIUniversität StuttgartStuttgartGermany
  2. 2.Center of PhysicsUniversity of MinhoBragaPortugal
  3. 3.Beijing Computational Science Research CenterBeijingChina

Personalised recommendations