Competing orders in one-dimensional half-integer fermionic cold atoms: A conformal field theory approach

Abstract

The physical properties of arbitrary half-integer spins F = N − 1/2 fermionic cold atoms loaded into a one-dimensional optical lattice are investigated by means of a conformal field theory approach. We show that for attractive interactions two different superfluid phases emerge for F ≥ 3/2: A BCS pairing phase, and a molecular superfluid phase which is formed from bound-states made of 2N fermions. In the low-energy approach, the competition between these instabilities and charge-density waves is described in terms of Z N parafermionic degrees of freedom. The quantum phase transition for F = 3/2, 5/2 is universal and shown to belong to the Ising and three-state Potts universality classes respectively. In contrast, for F ≥ 7/2, the transition is non-universal. For a filling of one atom per site, a Mott transition occurs and the nature of the possible Mott-insulating phases are determined. spins F = N − 1/2 fermionic cold atoms with s-wave scattering interactions loaded into a onedimensional optical lattice. The low-energy physical properties of 2F +1 = 2N -component fermions with contact interactions are known to be described by a Hubbard-like Hamiltonian [5]:where c † α,i (α = 1, ..., 2N ) is the fermion creation operator corresponding to the 2F + 1 = 2N atomic states and n i = α c † α,i c α,i is the density operator on site i. The pairing operators in Eq. (1) are defined through the Clebsch-Gordan coefficients for forming a total spin J from two spin-F fermions: P † JM,i = αβ JM |F, F ; αβ c † α,i c † β,i . The interactions are SU(2) spin-conserving and depend on U J parameters corresponding to the total spin J which takes only even integers value due to Pauli's principle: J = 0, 2, ..., 2N − 2. Even in this simple scheme the interaction pattern is still involved since there are N coupling constants in the general spin-F case. In this paper, we shall consider a two coupling-constant version of model (1) which incorporates the relevant physics of higher-spin degeneracy with respect to the formation of an exotic MS phase. To this end, it is enlightening to express this model in terms of the density n i and the BCS singlet-pairing operator for spin-F which is defined by: P † 00,i =

Bound-state dynamics in one-dimensional multispecies fermionic systems

“…We found that these are likely to be stabilized in systems which display an enlarged symmetry at low-energies and are associated with emergent duality symmetries in the spin sector. Our results are in agreement with previous findings for three types of bound-states that were identified in the attractive SU(N) Hubbard model with N = 3 and N = 4 [15,[18][19][20][21] as well as for SP (N) models [12,14,16,17] in such a situation is then SU(q) × SO(j). For odd j the bound-state has a charge q and the unit of current is j.…”

“…Performing the necessary OPE and averaging over the spin degrees of freedom we find, for the bound-state wave function and the density operator, the corrections to (IV. 16) and (IV.17)…”

“…19). As discussed in ( [12], [16]) the latter Z N/2 symmetry plays a crucial role in the low-energy limit and the associated excitations are related to that of generalized two-dimensional Z N/2…”

“…These bound-states were studied in Refs. ( [12,14,16,17]) in the context of cold fermionic atoms with hyperfine spin F = (N − 1)/2. In the following we shall review some of these previous findings in the light of the present work.…”

Phase diagrams of one-dimensional half-filled two-orbitalSU(N)cold fermion systems

“…,N − 1) describe the long-distance correlations of σ k r at the critical point [114]. In the context of cold atoms, the Z N CFT is also very useful to map out the zero-temperature phase diagram of general 1D higher-spin cold fermions [14,62,116].…”