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Schematic of the tripartite entanglement between the three spin blocks of a Heisenberg spin-1 chain with single-ion anisotropy. Here, we plot the absolute value of the fundamental SL(3, C) ⊗3 invariant I 6 for D = 2.5 after the ninth, tenth and eleventh steps of renormalization, which corresponds to a spin chain of size N = 3 n and three spin blocks of size 3 n−1 with n = 10, 11 and 12 respectively. The quantum phase transition point which separates the Néel and large-D phases is determined by the crossing of |I 6 | for different steps of renormalization.

Schematic of the tripartite entanglement between the three spin blocks of a Heisenberg spin-1 chain with single-ion anisotropy. Here, we plot the absolute value of the fundamental SL(3, C) ⊗3 invariant I 6 for D = 2.5 after the ninth, tenth and eleventh steps of renormalization, which corresponds to a spin chain of size N = 3 n and three spin blocks of size 3 n−1 with n = 10, 11 and 12 respectively. The quantum phase transition point which separates the Néel and large-D phases is determined by the crossing of |I 6 | for different steps of renormalization.

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FIG. 1. Schematic of the phase diagram for a spin-1 Heisenberg XXZ...
FIG. 2. Schematic of the quantum renormalization group (QRG) procedure....
FIG. 3. Schematic of the tripartite entanglement between the three spin...
FIG. 4. Schematic of the tripartite entanglement between the three spin...
FIG. 5. Schematic of the tripartite entanglement between the three spin...
Genuine tripartite entanglement as a probe of quantum phase transitions in a spin-1 Heisenberg chain with single-ion anisotropy
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  • Jun 2021
We study the quantum phase transitions of spin-1 Heisenberg chains with an easy-axis anisotropy $\Delta$ and a uniaxial single-ion anisotropy $D$ using a multipartite entanglement approach. The genuine tripartite entanglement between the spin blocks, measured by the tripartite qutrit hyperdeterminant, is calculated within the quantum renormalizatio...
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Context 1
... in Fig. 4, we plot the absolute value of the fundamental invariant I 6 as a function of ∆ for the low-lying energy state |ψ 0 with D = 2.5. The result shows that the are two different phases, namely the large-D and the antiferromagnetic Néel phases, both of which are characterized by a vanishing |I 6 |. The quantum phase transition between the ...
Context 2
... in Fig. 4, we plot the absolute value of the fundamental invariant I 6 as a function of ∆ for the low-lying energy state |ψ 0 with D = 2.5. The result shows that the are two different phases, namely the large-D and the antiferromagnetic Néel phases, both of which are characterized by a vanishing |I 6 |. The quantum phase transition between the ...