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arXiv:2412.20765 · SciPost Physics

Symmetry-enforced minimal entanglement and correlation in quantum spin chains

Kangle Li, Liujun Zou

Published Jul 17, 2025• 0 citations
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Abstract

The interplay between symmetry, entanglement and correlation is an interesting and important topic in quantum many-body physics. Within the framework of matrix product states, in this paper we study the minimal entanglement and correlation enforced by the SO(3) S O ( 3 ) spin rotation symmetry and lattice translation symmetry in a quantum spin- J J chain, with J J a positive integer. When neither symmetry is spontaneously broken, for a sufficiently long segment in a sufficiently large closed chain, we find that the minimal Rényi- \alpha α entropy compatible with these symmetries is \min\{ -\frac{2}{\alpha-1}\ln(\frac{1}{2^\alpha}({1+\frac{1}{(2J+1)^{\alpha-1}}})), 2\ln(J+1) \} min { − 2 α − 1 ln ( 1 2 α ( 1 + 1 ( 2 J + 1 ) α − 1 ) ) , 2 ln ( J + 1 ) } , for any \alpha∈\mathbb{R}^+ α ∈ ℝ + . In an infinitely long open chain with such symmetries, for any \alpha∈\mathbb{R}^+ α ∈ ℝ + the minimal Rényi- \alpha α entropy of half of the system is \min\{ -\frac{1}{\alpha-1}\ln(\frac{1}{2^\alpha}({1+\frac{1}{(2J+1)^{\alpha-1}}})), \ln(J+1) \} min { − 1 α − 1 ln ( 1 2 α ( 1 + 1

DOI
10.21468/scipostphys.19.1.020

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The interplay between symmetry, entanglement and correlation is an interesting and important topic in quantum many-body physics. Within the framework of matrix product states, in this paper we study the minimal entanglement and correlation enforced by the SO(3) S O ( 3 ) spin rotation symmetry and lattice translation symmetry in a quantum spin- J J chain, with J J a positive integer. When neither symmetry is spontaneously broken, for a sufficiently long segment in a sufficiently large closed chain, we find that the minimal Rényi- \alpha α entropy compatible with these symmetries is \min{ -\frac{2}{\alpha-1}\ln(\frac{1}{2^\alpha}({1+\frac{1}{(2J+1)^{\alpha-1}}})), 2\ln(J+1) } min { − 2 α − 1 ln ( 1 2 α ( 1 + 1 ( 2 J + 1 ) α − 1 ) ) , 2 ln ( J + 1 ) } , for any \alpha∈\mathbb{R}^+ α ∈ ℝ + . In an infinitely long open chain with such symmetries, for any \alpha∈\mathbb{R}^+ α ∈ ℝ + the minimal Rényi- \alpha α entropy of half of the system is \min{ -\frac{1}{\alpha-1}\ln(\frac{1}{2^\alpha}({1+\frac{1}{(2J+1)^{\alpha-1}}})), \ln(J+1) } min { − 1 α − 1 ln ( 1 2 α ( 1 + 1
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