Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

Abstract

The ferrimagnetic phase of the sawtooth chain with mixed ferromagnetic nearest-neighbour interactions JJ and antiferromagnetic next-nearest-neighbour interactions J'J′ (within the isotropic Heisenberg model) was previously characterized as a phase with commensurate order. In this paper, we demonstrate that the system in fact exhibits an incommensurate quantum spin spiral. Even though the ground state is translationally invariant in terms of the local spin expectations ‹S_i›‹Si#8250;, the spiral can be detected via the connected spin-spin correlations ‹{S_i\cdot S_j}#8250;‹Si⋅Sj#8250;-‹{S_i}#8250;\cdot‹{S_j}#8250;‹Si#8250;⋅‹Sj#8250; between the apical spins. It has a long wavelength that grows with J'J′ and that soon exceeds finite-system sizes typically employed in numerical simulations. A faithful treatment thus requires the use of state-of-the-art simulations for large, periodic systems. In this work, we are able to accurately treat up to L=400L=400 sites (200 unit cells) with periodic boundary conditions using the density-matrix renormaliztion group (DMRG). Exploiting the SU(2) symmetry allows us to directly compute the lowest-energy state for a given total spin. Our results are corroborated by variational uniform matrix product state (VUMPS) calculations, which work directly in the thermodynamic limit at the cost of a lower accuracy.

Magnetic properties of delta- and kagome-like chains with competing interactions

“…Equation ( 16) gives the estimate for the total spin of the ground state S tot ≃ 0.55N (γ ≪ 1) at h = 0, which is in very good agreement with the ground state spin S tot ≃ 0.54N obtained by numerical calculations [24]. Therefore, the value of S tot ≃ 0.54N in the s a = s b = 1 2 delta chain model slightly exceeds the value of magnetization S tot = 0.5N at the critical point.…”

“…The question arises about a nature of the ground state and the magnetic properties of the F-AF delta-chain at α > α c and their dependence on spin values s a and s b . For example, the s = 1 2 F-AF delta chain has the ferrimagnetic ground state in the whole region α > α c as it was shown in [23,24] on the base of numerical calculations. But the structure of this state is not quite clear especially for α ≫ 1.…”

Magnetic properties of ferro-antiferromagnetic spin triangle chain

“…. In regime J ≪ γ the corresponding upper and lower fields of the plateau are given by equations (10) and (11). The results for a dependence of the plateau width (or h c2 and h c1 ) on J are presented in figure 16 for some representative value of parameter α.…”

“…The delta-chain with both isotropic antiferromagnetic (AF) interactions J 1 > 0 and J 2 > 0 is well studied and has a number of interesting properties [4][5][6][7][8][9][10]. At the same time, the delta-chain with the competing ferro (F) -and AF interactions (J 1 < 0, J 2 > 0) (the F-AF delta-chain) is very interesting as well and attract interest recently [11][12][13][14][15][16][17][18][19][20][21]. The F-AF delta-chain describes real compounds, in particular, malonate-bridged copper complexes [22,23], kagome fluoride Cs 2 LiTi 3 F 12 [24] and cyclic complexes Fe 10 Gd 10 [25].…”