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Integrable model of a p -wave bosonic superfluid

Profile image of Jorge DukelskyJorge Dukelsky

2019, Physical Review Research

https://doi.org/10.1103/PHYSREVRESEARCH.1.032021
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Abstract

We present an exactly-solvable p-wave pairing model for two bosonic species. The model is solvable in any spatial dimension and shares some commonalities with the p+ip Richardson-Gaudin fermionic model, such as a third order quantum phase transition. However, contrary to the fermionic case, in the bosonic model the transition separates a gapless fragmented singlet pair condensate from a pair Bose superfluid, and the exact eigenstate at the quantum critical point is a pair condensate analogous to the fermionic Moore-Read state.

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References (38)

  1. L. Amico, A. Di Lorenzo, and A. Osterloh, Phys. Rev. Lett. 86, 5759 (2001).
  2. J. Dukelsky, C. Esebbag, and P. Schuck, Phys. Rev. Lett. 87, 066403 (2001).
  3. G. Sierra, J. Dukelsky, G. G. Dussel, J. von Delft, and F. Braun, Phys. Rev. B 61, R11890 (2000).
  4. R. W. Richardson, Phys. Lett. 3, 277 (1963).
  5. J. Dukelsky, S. Pittel, and G. Sierra, Rev. Mod. Phys. 76, 643 (2004).
  6. G. Ortiz, R. Somma, J. Dukelsky, and S. M. A. Rom- bouts, Nucl. Phys. B 707, 421 (2005).
  7. R. W. Richardson, Phys. Rev. 141, 949 (1966).
  8. G. Ortiz and J. Dukelsky, Phys. Rev. A 72, 043611 (2005).
  9. J. Dukelsky, G. Ortiz, S. M. A. Rombouts, and K. Van Houcke, Phys. Rev. Lett. 96, 180404 (2006).
  10. M. Bortz, S. Eggert, and J. Stolze, Phys. Rev. B 81, 035315 (2010).
  11. J. Dukelsky, G. G. Dussel, C. Esebbag, and S. Pittel, Phys. Rev. Lett. 93, 050403 (2004).
  12. D. A. Rowlands, and A. Lamacraft, Phys. Rev. Lett. 120, 090401 (2018).
  13. M. I. Ibañez, J. Links, G. Sierra, and S. Y. Zhao, Phys. Rev. B 79, 180501(R) (2009).
  14. S. M. A. Rombouts, J. Dukelsky, and G. Ortiz, Phys. Rev. B 82, 224510 (2010).
  15. G. Ortiz, J. Dukelsky, E. Cobanera, C. Esebbag, and C. Beenakker, Phys. Rev. Lett. 113, 267002 (2014).
  16. J. Links, I. Marquette, and A. Moghaddam, J. Phys. A: Math. Theor. 48 (2015) 374001.
  17. M. Van Raemdonck, S. De Baerdemacker, and D. Van Neck, Phys. Rev. B 89, 155136 (2014).
  18. G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991).
  19. N. Read and D. Green, Phys. Rev. B 61, 10267 (2000).
  20. G. Ortiz, Z. Nussinov, J. Dukelsky, and A. Seidel, Phys. Rev. B 88, 165303 (2013).
  21. R. W. Richardson, J. Math. Phys. 9, 1327 (1967).
  22. J. Dukelsky and P. Schuck, Phys. Rev. Lett. 86, 4207 (2001).
  23. F. Pan and J. P. Draayer, Nucl. Phys. A 636, 156 (1998).
  24. J. Dukelsky and S. Pittel, Phys. Rev. Lett. 86, 4791 (2001).
  25. F. Pan and J. P. Draayer, Phys. Lett. B 451, 1 (1999).
  26. S. Lerma H. and J. Dukelsky, Nucl. Phys. B 870, 421 (2013).
  27. S. Papp, J. Pino, and C. Wieman, Phys. Rev. Lett. 101, 040402 (2008).
  28. S. Dong, Y. Cui, C. Shen, Y. Wu, M. K. Tey, L. You, and B. Gao, Phys. Rev. A 94, 062702 (2016).
  29. L. Radzihovsky and S. Choi, Phys. Rev. Lett. 103, 095302 (2009).
  30. Z. Li, J.-S. Pan, and W. Vincent Liu, arXiv:1905.08463.
  31. A. B. Kuklov and B.V. Svistunov, Phys. Rev. Lett. 89, 170403 (2002).
  32. S. Ashhab and A. J. Leggett, Phys. Rev. A 68, 063612 (2003).
  33. S. Lerma H., S. M. A. Rombouts, J. Dukelsky, and G. Ortiz, Phys. Rev. B 84, 100503(R) (2011).
  34. E. Stouten, P. W. Claeys, J.-S. Caux, and V. Gritsev, Phys. Rev. B 99, 075111 (2019).
  35. D. S. Petrov, Phys. Rev. Lett. 115, 155302 (2015).
  36. H. Kadau et. al., Nature 530, 194 (2016).
  37. G. Semeghini et. al., Phys. Rev. Lett. 120, 235301 (2018).
  38. C. R. Cabrera et. al., Science 359, 301 (2018).

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