Competing orders in the generalized Hund chain model at half filling

Abstract

By using a combination of several nonperturbative techniques-a one-dimensional field theoretical approach together with numerical simulations using density-matrix renormalization group-we present an extensive study of the phase diagram of the generalized Hund model at half filling. This model encloses the physics of various strongly correlated one-dimensional systems, such as two-leg electronic ladders, ultracold degenerate fermionic gases carrying a large hyperfine spin 3 2 , other cold gases such as ytterbium 171 or alkaline-earth condensates. A particular emphasis is laid on the possibility to enumerate and exhaust the eight possible Mott-insulating phases by means of a duality approach. We exhibit a one-to-one correspondence between these phases and those of the two-leg electronic ladders with interchain hopping. Our results obtained from a weak-coupling analysis are in remarkable quantitative agreement with our numerical results carried out at moderate coupling.where l =1,2 is the leg or orbital index and = ↑ , ↓ denotes the spin-1 2 index. Three basic global continuous symmetries are retained: a U͑1͒ charge symmetry ͑c l,i → e i c l,i ͒, a SU͑2͒ spin-rotational invariance ͓c l,i → ͚ Ј ͑e i ជ · ជ /2 ͒ Ј c l Ј ,i , ជ being the Pauli matrices͔, and a U͑1͒ orbital symmetry ͑c 1͑2͒,i → e Ϯi c 1͑2͒,i ͒. Moreover, we will consider models for which the two legs or two bands behave identically; in other words, we impose a Z 2 invariance under the permutation of the legs. If we restrict ourselves to on-site interactions, the most general model with H =U͑1͒ c ϫ SU͑2͒ s ϫ U͑1͒ o ϫ Z 2 invariance then reads as follows: 32 l␤,i ͑2͒ whereas T i z = 1 2 ͚ ͑n 1,i − n 2,i ͒ is the generator of the U͑1͒ symmetry for orbital degrees of freedom.Model ͑1͒ depends on three microscopic couplings: a Coulombic interaction U, a Hund coupling J H , and an "orbital crystal-field anisotropy" J t . When J t = 0, the resulting model is the so-called Hund model which has been investigated in the context of orbital degeneracy. 15,28,32 The generalized Hund model ͑1͒ is directly linked to ultracold fermionic 171 Yb and alkaline-earth atoms with nuclear spin I = 1 2 . 33,34 The two-orbital states are described in these systems by the ground state ͑ 1 S 0 ϵ g͒ and a long-lived excited state ͑ 3 P 0 ϵ e͒. The almost perfect decoupling of the nuclear spin from the electronic angular momentum J in the two e , g states ͑J = 0 states͒ makes the s-wave scattering lengths of the problem independent of the nuclear spin. The low-energy Hamiltonian relevant to the 171 Yb cold gas loaded into a 1D optical lattice then reads 34 H Yb = − t ͚

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

“…In the latter case, the RG analysis has been done in detail already in Refs. [44,101], where the phase diagram of the generalized Hund and g-e cold fermions have been mapped out. We thus assume N > 2 hereafter and, for completeness, we will also determine the phase diagram of the half-filled p-band model (29) for N = 2 (see Appendix D).…”

“…In this respect, for the DMRG calculations of Sec. V, we will set t g = t e = t, U gg = U ee = U mm , and μ g = μ e to get the following Hamiltonian (generalized Hund model) [44]:…”

Symmetry-protected topological phase transition in one-dimensional Kondo lattice and its realization with ultracold atoms

“…As a result, the topological phase of the 1D Kondo lattice fits into the Z 4 classification of interacting fermionic SPT phases protected by the inversion symmetry in addition to the charge conservation. [40][41][42] The fermionic aspects of the SPT phase in the present setup can be contrasted to previous studies on realization of correlated SPT phases in cold alkaline-earth atoms, [43][44][45][46][47][48][49][50][51][52] where only the strongcoupling limit and thus spin-chain models were considered.…”

Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases

“…The model (45) with U gg = U ee , µ (g) = µ (e) is dubbed the generalized Hund model and has been studied extensively for N = 2 in the cold-fermion context [104,105]. It is obvious that, when t g = t e , J = J z = U diff = 0, µ g = µ e , the Hamiltonian H g-e is U(2N )-invariant and the orbital part (J and J z ) breaks it down to the generic symmetry U(1) c ×SU(N ) s ×U(1) o :…”