Density imbalanced mass asymmetric mixtures in one dimension

Click here to load reader

  • date post

    13-Jan-2016
  • Category

    Documents

  • view

    19
  • download

    0

Embed Size (px)

description

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). - PowerPoint PPT Presentation

Transcript of Density imbalanced mass asymmetric mixtures in one dimension

  • Density imbalanced mass asymmetric mixtures in one dimension Evgeni Burovski

    LPTMS, Orsay Giuliano Orso Thierry JolicoeurFERMIX-09, Trento

  • Effective low-energy theory,a.k.a. ``bosonizationTwo-component mixtures: use pseudo-spin notation =, (Haldane, 81)

  • Effective low-energy theory, contdEffect of interactions:

    higher harmonics

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

  • Is this cos() operator relevant? Renormalization group analysis ( Penc and Slyom, 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 phaseNotice the strong asymmetry between and

  • Quasi long range orderIn 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

  • A microscopic example: -species: free fermions:

    -species: dipolar bosons, a Luttinger liquid with ( Citro et al., 2007 )asTake a majority of light non-interacting fermions and a minority of heavy dipolar bosons:

    Switch on the coupling:

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

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

  • The asymmetric Hubbard model, correlations unequal hoppings: the model is no longer integrable, hence use DMRGsuperconducting correlationsMajority of the heavy species: YESMajority of the light species: NO

  • The asymmetric Hubbard model, correlations superconducting correlationsincommensurate densitiesMajority of the heavy species: YESMajority of the light species: NO unequal hoppings: the model is no longer integrable, hence use DMRG

  • The asymmetric Hubbard model, contd long-range behavior is the same for equal masses unequal masses, incommensurate densitiesBroadening of the momentum distribution is insensitive to the commensurability

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

  • 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