scholarly journals Maximized string order parameters in the valence bond solid states of quantum integer spin chains

2009 ◽  
Vol 42 (28) ◽  
pp. 285202
Author(s):  
Hong-Hao Tu ◽  
Guang-Ming Zhang ◽  
Tao Xiang
Keyword(s):  
Valence Bond ◽  
Order Parameters ◽  
Spin Chains ◽  
Solid States ◽  
Integer Spin ◽  
Quantum Integer ◽  
Valence Bond Solid

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.

Breakdown of the Spin-1 Haldane Phase Via Quantum Fluctuations

1998 ◽  
Vol 12 (18) ◽  
pp. 1795-1808 ◽  
Author(s):  
Shoji Yamamoto
Keyword(s):  
Wave Function ◽  
Short Range ◽  
Valence Bond ◽  
Quantum Fluctuations ◽  
Bound State ◽  
Spin Chains ◽  
Repulsive Interaction ◽  
Variational Parameter ◽  
Valence Bond Solid ◽  
Antiferromagnetic Spin

Investigating quantum fluctuations in the ground states of S=1 quantum antiferromagnetic spin chains described by the bilinear-biquadratic Hamiltonian ℋ=∑i [Si·Si+1+β (Si·Si+1)2], we study a mechanism of the breakdown of the Haldane phase. Based on the valence-bond-solid structure, but replacing two links of them by triplet bonds (crackions), we construct a trial wave function which is singlet and translationally invariant, where the crackion-crackion distance is regarded as a variational parameter. At β < 1/3, the minimization of the variational energy results in a bound state of crackions, while at β > 1/3, crackions come to be set free from their bound state with increase of β and the chain length. We point out that the breakdown of the Haldane phase with β approaching 1 can be attributed to the collapse of the bound state and the growth of a short-range repulsive interaction between crackions.

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