ENTANGLEMENT IN VALENCE-BOND-SOLID STATES

This article reviews the quantum entanglement in Valence-Bond-Solid (VBS) states defined on a lattice or a graph. The subject is presented in a self-contained and pedagogical way. The VBS state was first introduced in the celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki (abbrevia...

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Published inInternational journal of modern physics. B, Condensed matter physics, statistical physics, applied physics Vol. 24; no. 11; pp. 1361 - 1440
Main Authors KOREPIN, VLADIMIR E., XU, YING
Format Journal Article
LanguageEnglish
Published World Scientific Publishing Company 30.04.2010
Subjects
entropy
density matrix
AKLT
VBS
entanglement
quantum spins
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ISSN0217-9792
1793-6578
DOI10.1142/S0217979210055676

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Summary:This article reviews the quantum entanglement in Valence-Bond-Solid (VBS) states defined on a lattice or a graph. The subject is presented in a self-contained and pedagogical way. The VBS state was first introduced in the celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki (abbreviation AKLT is widely used). It became essential in condensed matter physics and quantum information (measurement-based quantum computation). Many publications have been devoted to the subject. Recently entanglement was studied in the VBS state. In this review, we start with the definition of a general AKLT spin chain and the construction of VBS ground state. In order to study entanglement, a block subsystem is introduced and described by the density matrix. Density matrices of 1-dimensional models are diagonalized and the entanglement entropies (the von Neumann entropy and Rényi entropy) are calculated. In the large block limit, the entropies also approach finite limits. Study of the spectrum of the density matrix led to the discovery that the density matrix is proportional to a projector.
ISSN:0217-9792
1793-6578
DOI:10.1142/S0217979210055676