Spontaneous trimerization in a bilinear-biquadraticS=1zig-zag chain

Abstract

Recent theoretical studies raised the possibility of a realization of spin nematic states in the S = 1 triangular lattice compound NiGa 2 S 4 . We study the bilinear-biquadratic spin 1 chain in a zig-zag geometry by means of the density matrix renormalization group method and exact diagonalization. We present the phase diagram focusing on antiferromagnetic interactions. Adjacent to the known Haldane-double Haldane and the extended critical phase with dominant spin nematic correlations we find a trimerized phase with a nonvanishing energy gap. We discuss results for different order parameters, energy gaps, correlation functions, and the central charge, and make connection to field theoretical predictions for the phase diagram.

Exact models for trimerization and tetramerization in spin chains

“…61 As proposed by Corboz et al, 46 the existence of a tetramerized phase was verified for the regime J 1 Ϸ J 2 . 60,61…”

“…As a possible generalization, we might look for models of spin S antiferromagnets with an SU͑2S +1͒ symmetry, i.e., models in which n =2S + 1 spins might form an n-mer rather than three neighboring spins a trimer. Corboz et al 46 advocated that such an n-merized phase should appear in an appropriate J 1 − J 2 model provided the ratio J 1 / J 2 exceeds a certain critical value. Note that this is not in contradiction to our previous statement that n + 1-site interactions are required for tetramerization.…”

“…Sólyom and Zittartz 45 presented such a model with four-site interaction. In this model, 46 investigated numerically the bilinear-biquadratic Heisenberg model with nearest-and next-nearest-neighbor interactions:…”

Bose metals and insulators on multileg ladders with ring exchange

“…(22) with θ = π/4, λ = 0, and J ⊥ = 0 is equivalent to the SU(3) symmetric Heisenberg model, i.e., the spin-1 LaiSutherland model, 60,61 which is known to be critical with c = 2 gapless modes. 58,[61][62][63][64] There is also known to be an extended critical phase in this model, still at λ = 0 and J ⊥ = 0, but away from the SU(3) point in the parameter range θ ∈ [π/4, π/2). 58,62,64,65 Interestingly, this critical phase has soft modes 64 at q x = 0, ±2π/3 with dominant spin quadrupolar correlations at wave vector 2π/3, 58 which is precisely the "2k F " wave vector in the J = J ⊥ = 0 limit of our DBL [3,0] theory (i.e., three equally filled d 1 bands) at which we should expect singularities in, e.g., D b (q x , q y = ±2π/3).…”

“…58,[61][62][63][64] There is also known to be an extended critical phase in this model, still at λ = 0 and J ⊥ = 0, but away from the SU(3) point in the parameter range θ ∈ [π/4, π/2). 58,62,64,65 Interestingly, this critical phase has soft modes 64 at q x = 0, ±2π/3 with dominant spin quadrupolar correlations at wave vector 2π/3, 58 which is precisely the "2k F " wave vector in the J = J ⊥ = 0 limit of our DBL [3,0] theory (i.e., three equally filled d 1 bands) at which we should expect singularities in, e.g., D b (q x , q y = ±2π/3). It thus seems plausible that the well-known extended critical phase in the bilinear-biquadratic spin-1 chain 58 is connected to the decoupled chains limit of DBL [3,0], although we can't be sure without a direct study of Eq.…”