Advertisement

Quantum phase transitions and localization in semigroup Fredkin spin chain

  • Pramod PadmanabhanEmail author
  • Fumihiko Sugino
  • Vladimir Korepin
Article
  • 20 Downloads

Abstract

We construct an extended quantum spin chain model by introducing new degrees of freedom to the Fredkin spin chain. The new degrees of freedom called arrow indices are partly associated with the symmetric inverse semigroup \(\mathcal{S}^3_1\). Ground states of the model fall into three different phases, and quantum phase transition takes place at each phase boundary. One of the phases exhibits logarithmic violation of the area law of entanglement entropy and quantum criticality, whereas the other two obey the area law. As an interesting feature arising by the extension, there are excited states due to disconnections with respect to the arrow indices. We show that these states are localized without disorder.

Keywords

Entanglement entropy Localization Quantum statistical physics 

Notes

References

  1. 1.
    Kellendonk, J., Lawson, M.V.: Tiling semigroups. J. Algebra 224(1), 140–150 (2000)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Senechal, M.: Quasicrystals and Geometry. Cambridge University Press, Cambridge (1995)zbMATHGoogle Scholar
  3. 3.
    Exel, R., Goncalves, D., Starling, C.: The tiling \(C^*\)-algebra viewed as a tight inverse semigroup algebra. arXiv:1106.4535 [math.OA]
  4. 4.
    Padmanabhan, P., Rey, S.-J., Teixeira, D., Trancanelli, D.: Supersymmetric many-body systems from partial symmetries: integrability, localization and scrambling. JHEP 1705, 136 (2017). arXiv:1702.02091 [hep-th]
  5. 5.
    Sugino, F., Padmanabhan, P.: Area law violations and quantum phase transitions in modified Motzkin walk spin chains. J. Stat. Mech. 1801(1), 013101 (2018). arXiv:1710.10426 [quant-ph]
  6. 6.
    Bravyi, S., Caha, L., Movassagh, R., Nagaj, D., Shor, P.W.: Criticality without frustration for quantum spin-1 chains. Phys. Rev. Lett 109, 207202 (2012)ADSCrossRefGoogle Scholar
  7. 7.
    Movassagh, R., Shor, P.W.: Power law violation of the area law in quantum spin chains. Proc. Natl. Acad. Sci. 113, 13278–13282 (2016). arXiv:1408.1657 [quant-ph]
  8. 8.
    Dell’Anna, L., Salberger, O., Barbiero, L., Trombettoni, A., Korepin, V.E.: Violation of cluster decomposition and absence of light-cones in local integer and half-integer spin chains. Phys. Rev. B 94, 155140 (2016). arXiv:1604.08281 [cond-mat.str-el]
  9. 9.
    Salberger, O., Korepin, V.: Fredkin Spin Chain. Rev. Math. Phys. 29, 1750031 (2017). arXiv:1605.03842 [quant-ph]
  10. 10.
    Anderson, P.W.: Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492 (1958)ADSCrossRefGoogle Scholar
  11. 11.
    Basko, D.M., Aleiner, I.L., Altshuler, B.L.: Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states. Ann. Phys. (NY) 321, 1126 (2006). arXiv:cond-mat/0506617 [cond-mat.mes-hall]
  12. 12.
    Nandkishore, R., Huse, D.A.: Many body localization and thermalization in quantum statistical mechanics. Ann. Rev. Condens. Matter Phys. 6, 15 (2015). arXiv:1404.0686 [cond-mat.stat-mech]
  13. 13.
    Altman, E., Vosk, R.: Universal dynamics and renormalization in many body localized systems. Ann. Rev. Condens. Matter Phys. 6, 383 (2015). arXiv:1408.2834 [cond-mat.dis-nn]
  14. 14.
    Imbre, J.Z., Ros, V., Scardicchio, A.: Review: local integrals of motion in many-body localized systems. Ann. Phys. (Berlin) 529, 1600278 (2017). arXiv:1609.08076 [cond-mat.dis-nn]
  15. 15.
    Padmanabhan, P., Sugino, F., Korepin, V.: in preparationGoogle Scholar
  16. 16.
    Udagawa, T., Zhang, Z., Katsura, H., Klich, I., Korepin, V.: Deformed Fredkin spin chain with extensive entanglement. J. Stat. Mech. 1706(6), 063103 (2017). arXiv:1611.04983 [cond-mat.stat-mech]
  17. 17.
    Zhang, Z., Klich, I.: Entropy, gap and a multi-parameter deformation of the Fradkin spin chain. J. Phys. A Math. Theor. 50, 425201 (2017). arXiv:1702.03581 [cond-mat.stat-mech]
  18. 18.
    Zhang, Z., Ahmadain, A., Klich, I.: Quantum phase transition from bounded to extensive entanglement entropy in a frustration-free spin chain. arXiv:1606.07795 [quant-ph]
  19. 19.
    Udagawa, T., Katsura, H.: Finite-size gap, magnetization, and entanglement of deformed Fredkin spin chain. J. Phys. A Math. Theor. 50, 405002 (2017). arXiv:1701.00346 [cond-mat.stat-mech]
  20. 20.
    Caha, L., Nagaj, D.: The pair-flip model: a very entangled translationally invariant spin-chain. arXiv:1805.07168 [quant-ph]

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Pramod Padmanabhan
    • 1
    Email author
  • Fumihiko Sugino
    • 1
  • Vladimir Korepin
    • 2
  1. 1.Fields, Gravity & Strings, Center for Theoretical Physics of the UniverseInstitute for Basic Science (IBS)DaejeonRepublic of Korea
  2. 2.C.N.Yang Institute for Theoretical PhysicsStony Brook UniversityStony BrookUSA

Personalised recommendations