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