1 / 14

Density imbalanced mass asymmetric mixtures in one dimension

Density imbalanced mass asymmetric mixtures in one dimension. Evgeni Burovski. Thierry Jolicoeur. Giuliano Orso. LPTMS, Orsay. FERMIX-09, Trento. Effective low-energy theory,. a.k.a. ``bosonization’’. Two-component mixtures: use pseudo-spin notation σ= , . (Haldane, 81).

hoai
Download Presentation

Density imbalanced mass asymmetric mixtures in one dimension

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Density imbalanced mass asymmetric mixtures in one dimension Evgeni Burovski Thierry Jolicoeur Giuliano Orso LPTMS, Orsay FERMIX-09, Trento

  2. Effective low-energy theory, a.k.a. ``bosonization’’ Two-component mixtures: use pseudo-spin notation σ=,  (Haldane, 81)

  3. Non-interacting fermions: Effective low-energy theory, cont’d Effect of interactions: • higher harmonics

  4. The effect of higher harmonics ( p and q are integers ) p =q = 1  spin gap (attractive interactions)

  5. massive massless A sufficient condition: Is this cos(…) operator relevant? • Renormalization group analysis ( Penc and Sólyom, 1990 ; Mathey, 2007) : • cos(…) is either relevant or irrelevant in the RG sence. • cos(…) is irrelevant  1D FFLO phase : gapless, • all correlations are algebraic, • cos(…) is relevant  ‘massive’ phase Notice the strong asymmetry between  and 

  6. Quasi long range order In 1D no true long-range order is possible  algebraic correlations at most: i.e. the slowest decay  the dominant instability. • Equal densities ( p = q = 1 ), attractive interactions : • Unequal densities ( e.g. p = 2, q = 1 ) : • CDW/ SDW-z correlations are algebraic • SS correlations are destroyed (i.e. decay exponentially) • “trimer’’ ordering

  7. I. e.: (an infinitesimal attraction) opens the gap. A microscopic example: • -species: free fermions: • -species: dipolar bosons, a Luttinger liquid with ( Citro et al., 2007 ) as • Take a majority of light non-interacting fermions and • a minority of heavy dipolar bosons: Switch on the coupling:

  8. The Hubbard model • spin-independent hopping: Bethe-Ansatz solvable ( Orso, 2007; Hu et al., 2007) • two phases: fully paired (“BCS”) and partially polarized (“FFLO”) “FFLO” “BCS” ( cf. B. Wang et al., 2009 ) 1 component gas

  9. The asymmetric Hubbard: few-body unequal hoppings: three-body bound states exist in vacuum (e.g., Mattis, 1986) pair energy What about many-body physics?

  10. ‘commensurate’ densities The asymmetric Hubbard model, correlations unequal hoppings: the model is no longer integrable, hence use DMRG superconducting correlations Majority of the heavy species: YES Majority of the light species: NO

  11. ‘commensurate’ densities The asymmetric Hubbard model, correlations unequal hoppings: the model is no longer integrable, hence use DMRG superconducting correlations ‘incommensurate’ densities Majority of the heavy species: YES Majority of the light species: NO

  12. The asymmetric Hubbard model, cont’d Broadening of the momentum distribution is insensitive to the commensurability • long-range behavior is the same for • equal masses • unequal masses, incommensurate densities

  13. The asym. Hubbard model, phase diagram Multiple commensurate phases at low density

  14. Conclusions and outlook • Multiple partially gapped phases possible in density- and mass-imbalanced mixtures. • (Quasi-)long-range ordering of several-particle composites • D > 1 ? • Li-K mixtures ? Mo’ info: EB, GO, and TJ, arXiv:0904.0569

More Related