Ground-state phase diagram of a spin-12frustrated ferromagnetic XXZ chain: Haldane dimer phase and gapped/gapless chiral phases

Abstract

The ground-state phase diagram of a spin-1 2 XXZ chain with competing ferromagnetic nearestneighbor (J1 < 0) and antiferromagnetic second-neighbor (J2 > 0) exchange couplings is studied by means of the infinite time evolving block decimation algorithm and effective field theories. For the SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the range −4 < J1/J2 < 0 has a small but finite ferromagnetic dimer order. We argue that this spontaneous dimer order is associated with effective spin-1 degrees of freedom on dimerized bonds, which collectively form a valence bond solid state as in the spin-1 antiferromagnetic Heisenberg chain (the Haldane spin chain). We thus call this phase the Haldane dimer phase. With easy-plane anisotropy, the model exhibits a variety of phases including the vector chiral phase with gapless excitations and the even-parity dimer and Néel phases with gapped excitations, in addition to the Haldane dimer phase. Furthermore, we show the existence of gapped phases with coexisting orders in narrow regions that intervene between the gapless chiral phase and any one of Haldane dimer, even-parity dimer, and Néel phases. Possible implications for quasi-one-dimensional edge-sharing cuprates are discussed.

Vector-spin-chirality order in a dimerized frustrated spin-12chain

“…It has been shown that in the case of δ = 0 (γ xy δ = γ z± δ = 0) and g = 0 (γ ssc = γ ′ ssc = 0), the gapless chiral phase can appear as the coupling constant γ tw grows on the renormalization group flow for a certain range of J 1 /J 2 < 0 and 0 < ∆ < 1 [Refs. 10,23]. The bond alternation of J 1 immediately locks the field √ 4πφ + to either 0 or π depending on the sign of J 1 δ and uniformly shifts the locking position of √ 4πθ − from ±π/2, since it provides relevant interactions with the coupling constants γ xy δ and γ z+ δ .…”

“…(22), (23), and (24) hold at least for gh = 0. Then, we expand the self-consistent equations of the mean-field decoupling approximation, Eqs.…”

“…This yields a coexistence of the vectorchiral and dimer orders characterized by sin √ 4πθ − = 0 and ( cos √ 4πθ − , cos √ 4πφ + ) = 0, respectively, while the Neel LRO is absent, i.e., ∂ x φ − = sin √ 4πφ + = 0. As far as the fields are locked, we can rely on a mean-field approximation to decouple the ± sectors 10,23 . Then, the Hamiltonian density is written as H ≈ H 0 + H + + H − with…”

“…23, which we will classify as distinct symmetry-protected topological phases 24,25 in the absence of the Neel order. (i) One is a Haldane dimer state 23 , that is, a Haldane state 26,27 formed by spin triplet pairs of the ferromagneticallycoupled nearest-neighbor spins, as it appears in the vicinity of the SU(2)-symmetric case 23,28 . (ii) The other is an even-parity dimer state realized with large enough easyplane magnetic anisotropy.…”

Crossover from an incommensurate singlet spiral state with a vanishingly small spin gap to a valence-bond solid state in dimerized frustrated ferromagnetic spin chains

“…This is consistent with a maximun gap around α = 0.6 at weak dimerization (β = 0.9). On the other hand, an adiabatic connection of the AKLT-type VBS state from β = 0 to 1 was predicted by the field-theoretical analysis for |J 1 | J 2 [29]. A contour plot of the magnitude of ∆ is given in Figure 2.…”