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arXiv:2606.28000

Ferrimagnetic and Haldane-type phases in a mixed-spin $1$-$\tfrac{1}{2}$-$\tfrac{1}{2}$ quantum trimer chain

A. Felinto, R. R. Montenegro-Filho

Published Jun 26, 2026• 0 citations
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Abstract

Bipartite Lieb-Mattis ferrimagnetism and the symmetry-protected Haldane phase are paradigmatic mechanisms in quasi-one-dimensional quantum magnets. Both emerge, in distinct regimes, in a mixed-spin $1$-$\tfrac{1}{2}$-$\tfrac{1}{2}$ Heisenberg trimer chain with antiferromagnetic backbone exchange $J$ and a side spin-$\tfrac{1}{2}$ coupled to each backbone spin by an exchange $J_t$ of either sign. Using the density matrix renormalization group, we compute magnetization curves and the entanglement spectrum and entropy. For $J_t>0$ a robust ferrimagnetic plateau forms at magnetization per unit cell $m=1$, whose multiplet entropy reflects how the conserved magnetization splits between the halves. For $J_t<0$ an $m=0$ plateau opens and grows with $|J_t|$, while the $m=1$ plateau closes. As $J_t\to-\infty$ the chain maps onto a spin-$1$ Heisenberg chain with coupling $J/2$: the $m=0$ width $Δh\simeq 0.196$ matches half the Haldane gap. Exponentially localized spin-$\tfrac{1}{2}$ edge states and the even-fold degeneracy of the entanglement spectrum confirm the Haldane character of the $m=0$ phase.

DOI
10.48550/arxiv.2606.28000

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Magnetization curves of the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains are calculated with the help of density-matrix renormalization group method for several quantum spin numbers S=1, 3/2, 2 and 5/2.It is shown that the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains exhibit irrespective of the spin value S exactly one intermediate magnetization plateau, which can be identified with the gapped Lieb-Mattis ferrimagnetic ground state.The magnetization plateau due to the Lieb-Mattis ferrimagnetism breaks down at a quantum phase transition towards the Luttinger spin liquid, which is characterized by a continuous change of the magnetization with the magnetic field until another quantum critical point is reached at the saturation field.
The spin-1/2 Ising-Heisenberg branched chain composed of regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is rigorously solved in a magnetic field by the transfer-matrix approach. The ground-state phase diagram, the magnetization process and the concurrence measuring a degree of bipartite entanglement within the Heisenberg dimers are examined in detail. Three different ground states were found depending on a mutual interplay between the magnetic field and two different coupling constants: the modulated quantum antiferromagnetic phase, the quantum ferrimagnetic phase, and the classical ferromagnetic phase. Two former quantum ground states are manifested in zero-temperature magnetization curves as intermediate plateaus at zero and one-half of the saturation magnetization, whereas the one-half plateau disappears at a triple point induced by a strong-enough ferromagnetic Ising coupling. The ground-state phase diagram and zero-temperature magnetization curves of the analogous spin-1/2 Heisenberg branched chain were investigated using density-matrix renormalization group calculations. The latter fully quantum Heisenberg model involves, besides two gapful phases manifested as zero and one-half magnetization plateaus, gapless quantum spin-liquid phase. The intermediate one-half plateau of the spin-1/2 Heisenberg branched chain vanishes at Kosterlitz-Thouless quantum critical point between gapful and gapless quantum ground states unlike the triple point of the spin-1/2 Ising-Heisenberg branched chain.
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The ground-state phases of mixed diamond chains with (S,τ(1),τ(2))=(1/2,1/2,1)S, τ^{(1)}, τ^{(2)})=(1/2,1/2,1)S,τ(1),τ(2))=(1/2,1/2,1), where SSS is the magnitude of vertex spins, and τ(1)τ^{(1)}τ(1) and τ(2)τ^{(2)}τ(2) are those of apical spins, are investigated. The apical spins τ(1)τ^{(1)}τ(1) and τ(2)τ^{(2)}τ(2) are connected with each other by an exchange coupling λλλ. Other exchange couplings are set equal to unity. This model has an infinite number of local conservation laws. For large λλλ, the ground state is equivalent to that of the uniform spin 1/21/21/2 chain. Hence, the ground state is a gapless spin liquid. For λ≤0λ\leq 0λ≤0, the ground state is a Lieb-Mattis ferrimagnetic phase with spontaneous magnetization msp=1m_{\rm sp}=1msp​=1 per unit cell. For intermediate λλλ, we find a series of ferrimagnetic phases with msp=1/pm_{\rm sp}=1/pmsp​=1/p where ppp takes positive integer values. The phases with p≥2p \geq 2p≥2 are accompanied by the spontaneous breakdown of the ppp-fold translational symmetry. It is suggested that the phase with arbitrarily large ppp, namely infinitesimal spontaneous magnetization, is allowed as λλλ approaches the transition point to the gapless spin liquid phase.