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

A. Felinto, R. R. Montenegro-Filho

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.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.

arXiv:2606.28000Jun 26, 20260 citations

Entanglement in spin-1 Heisenberg XY chain

Meng Qin, YingJuan Tao, Ming‐Liang Hu +1 more

Science in China. Series G, Physics, mechanics & astronomy/Science in China. Series G, Physics, Mechanics & AstronomyJun 21, 200816 citations

Entanglement in a spin-s antiferromagnetic Heisenberg chain (4 pages)

Shannong Zhu, Xiaotao Hao

Physical Review AJan 1, 20050 citations

Ferrimagnetic and Haldane-type phases in a mixed-spin 1-12-12 quantum trimer chain

A. Felinto, R. R. Montenegro-Filho

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 $\Delta h\simeq 0.196$ 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.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 $\Delta h\simeq 0.196$ 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.

Physica B Condensed MatterAug 15, 20260 citations

Exact ground states for coupled spin trimers

Heinz–Jürgen Schmidt, Johannes Richter

We consider a class of geometrically frustrated Heisenberg spin systems which admit exact ground states. The systems consist of suitably coupled antiferromagnetic spin trimers with integer spin quantum numbers s and their ground state Φ will be the product state of the local singlet ground states of the trimers. We provide linear equations for the inter-trimer coupling constants which are equivalent to Φ being an eigenstate of the corresponding Heisenberg Hamiltonian and sufficient conditions for Φ being a ground state. The classical case s → ∞ can be completely analyzed. For the quantum case we consider a couple of examples, where the critical values of the inter-trimer couplings are numerically determined. These examples include chains of corner sharing tetrahedra as well as certain spin tubes. Φ is proven to be gapped in the case of trimer chains. This follows from a more general theorem on quantum chains with product ground states.We consider a class of geometrically frustrated Heisenberg spin systems which admit exact ground states. The systems consist of suitably coupled antiferromagnetic spin trimers with integer spin quantum numbers s and their ground state Φ will be the product state of the local singlet ground states of the trimers. We provide linear equations for the inter-trimer coupling constants which are equivalent to Φ being an eigenstate of the corresponding Heisenberg Hamiltonian and sufficient conditions for Φ being a ground state. The classical case s → ∞ can be completely analyzed. For the quantum case we consider a couple of examples, where the critical values of the inter-trimer couplings are numerically determined. These examples include chains of corner sharing tetrahedra as well as certain spin tubes. Φ is proven to be gapped in the case of trimer chains. This follows from a more general theorem on quantum chains with product ground states.

arXiv:1006.4299Journal of Physics A Mathematical and TheoreticalSep 16, 201012 citations

Ferrimagnetic and Haldane-type phases in a mixed-spin

1

\tfrac{1}{2}

\tfrac{1}{2}

quantum trimer chain

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

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.