Spin-Peierls, valence-bond solid, and Néel ground states of low-dimensional quantum antiferromagnets

1990 ◽  
Vol 42 (7) ◽  
pp. 4568-4589 ◽  
Author(s):  
N. Read ◽  
Subir Sachdev
Keyword(s):  
Valence Bond ◽  
Ground States ◽  
Quantum Antiferromagnets ◽  
Low Dimensional ◽  
Valence Bond Solid

scholarly journals Valence Bond Ground States in Isotropic Quantum Antiferromagnets

1988 ◽  
pp. 253-304 ◽  
Author(s):  
Ian Affleck ◽  
Tom Kennedy ◽  
Elliott H. Lieb ◽  
Hal Tasaki
Keyword(s):  
Valence Bond ◽  
Ground States ◽  
Quantum Antiferromagnets

EXACT GROUND STATES OF ONE-DIMENSIONAL VALENCE-BOND-SOLID HAMILTONIANS

1987 ◽  
Vol 01 (05n06) ◽  
pp. 231-237 ◽  
Author(s):  
P.L. Iske ◽  
W.J. Caspers
Keyword(s):  
Ground State ◽  
Valence Bond ◽  
Ground States ◽  
Open Chain ◽  
State Correlation ◽  
One Dimensional ◽  
Degenerate Ground State ◽  
Closed Chain ◽  
Ground State Correlation ◽  
Valence Bond Solid

The ground state(s) of a Hamiltonian, introduced by Affleck, Kennedy, Lieb and Tasaki, in connection with the Valence-Bond-Solid (VBS) states, are explicitly given for the spin-1 chains. The structure of these ground states is a rather simple one. For a closed chain we find a unique ground state; for the open chain we find a fourfold-degenerate ground state. The ground state correlation function for the ring is calculated.

scholarly journals MEASUREMENT-BASED QUANTUM COMPUTING WITH VALENCE-BOND-SOLIDS

2012 ◽  
Vol 26 (02) ◽  
pp. 1230002 ◽  
Author(s):  
LEONG CHUAN KWEK ◽  
ZHAOHUI WEI ◽  
BEI ZENG
Keyword(s):  
Quantum Computing ◽  
Information Science ◽  
Valence Bond ◽  
Ground States ◽  
Research Area ◽  
Many Body ◽  
Cluster States ◽  
Valence Bond Solid ◽  
Alternative Resource ◽  
Sequential Measurements

Measurement-based quantum computing (MBQC) is a model of quantum computing that proceeds by sequential measurements of individual spins in an entangled resource state. However, it remains a challenge to produce efficiently such resource states. Would it be possible to generate these states by simply cooling a quantum many-body system to its ground state? Cluster states, the canonical resource states for MBQC, do not occur naturally as unique ground states of physical systems. This inherent hurdle has led to a significant effort to identify alternative resource states that appear as ground states in spin lattices. Recently, some interesting candidates have been identified with various valence-bond-solid (VBS) states. In this review, we provide a pedagogical introduction to recent progress regarding MBQC with VBS states as possible resource states. This study has led to an interesting interdisciplinary research area at the interface of quantum information science and condensed matter physics.

scholarly journals Valence bond ground states in isotropic quantum antiferromagnets

1988 ◽  
Vol 115 (3) ◽  
pp. 477-528 ◽  
Author(s):  
Ian Affleck ◽  
Tom Kennedy ◽  
Elliott H. Lieb ◽  
Hal Tasaki
Keyword(s):  
Valence Bond ◽  
Ground States ◽  
Quantum Antiferromagnets
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