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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).

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Density imbalanced mass asymmetric mixtures in one dimension

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  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

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