scholarly journals Valence bond solid states with symplectic symmetry

2008 ◽  
Vol 78 (1) ◽  
Author(s):  
Dirk Schuricht ◽  
Stephan Rachel
Keyword(s):  
Valence Bond ◽  
Solid States ◽  
Valence Bond Solid

scholarly journals Supersymmetric valence bond solid states

2009 ◽  
Vol 79 (22) ◽  
Author(s):  
Daniel P. Arovas ◽  
Kazuki Hasebe ◽  
Xiao-Liang Qi ◽  
Shou-Cheng Zhang
Keyword(s):  
Valence Bond ◽  
Solid States ◽  
Valence Bond Solid

scholarly journals Entanglement in valence-bond-solid states on symmetric graphs

2010 ◽  
Vol 43 (25) ◽  
pp. 255303 ◽  
Author(s):  
Hosho Katsura ◽  
Naoki Kawashima ◽  
Anatol N Kirillov ◽  
Vladimir E Korepin ◽  
Shu Tanaka
Keyword(s):  
Valence Bond ◽  
Solid States ◽  
Symmetric Graphs ◽  
Valence Bond Solid

scholarly journals ENTANGLEMENT IN VALENCE-BOND-SOLID STATES

2010 ◽  
Vol 24 (11) ◽  
pp. 1361-1440 ◽  
Author(s):  
VLADIMIR E. KOREPIN ◽  
YING XU
Keyword(s):  
Density Matrix ◽  
Condensed Matter ◽  
Valence Bond ◽  
Von Neumann Entropy ◽  
Information Measurement ◽  
Von Neumann ◽  
Solid States ◽  
The Subject ◽  
Definition Of ◽  
Valence Bond Solid

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.

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