Entanglement and quantum phase transitions in matrix-product spin-1 chains

S. Alipour, V. Karimipour, L. Memarzadeh*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

22 Citations (Scopus)


We consider a one-parameter family of matrix-product states of spin-1 particles on a periodic chain and study in detail the entanglement properties of such a state. In particular, we calculate exactly the entanglement of one site with the rest of the chain, and the entanglement of two distant sites with each other, and show that the derivative of both these properties diverge when the parameter g of the states passes through a critical point. Such a point can be called a point of quantum phase transition, since at this point the character of the matrix-product state, which is the ground state of a Hamiltonian, changes discontinuously. We also study the finite size effects and show how the entanglement depends on the size of the chain. This later part is relevant to the field of quantum computation where the problem of initial state preparation in finite arrays of qubits or qutrits is important. It is also shown that the entanglement of two sites have scaling behavior near the critical point.

Original languageEnglish
Article number052322
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number5
Publication statusPublished - 17 May 2007
MoE publication typeA1 Journal article-refereed

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