Valence bond states on quantum spin chains as ground states with spectral gap

1991 ◽  
Vol 24 (4) ◽  
pp. L185-L189 ◽  
Author(s):  
M Fannes ◽  
B Nachtergaele ◽  
R F Werner
Keyword(s):  
Spectral Gap ◽  
Valence Bond ◽  
Ground States ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains

scholarly journals q-DEFORMATIONS OF QUANTUM SPIN CHAINS WITH EXACT VALENCE-BOND GROUND STATES

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3645-3654 ◽  
Author(s):  
M.T. BATCHELOR ◽  
C.M. YUNG
Keyword(s):  
Condensed Matter ◽  
Valence Bond ◽  
Ground States ◽  
Quantum Spin ◽  
Total Spin ◽  
Spin Chains ◽  
The Other ◽  
Condensed Matter Physics ◽  
Spin States ◽  
Quantum Spin Chains

Quantum spin chains with exact valence-bond ground states are of great interest in condensed-matter physics. A class of such models was proposed by Affleck et al., each of which is su(2)-invariant and constructed as a sum of projectors onto definite total spin states at neighboring sites. We propose to use the machinery of the q-deformation of su(2) to obtain generalisations of such models, and work out explicitly the two simplest examples. In one case we recover the known anisotropic spin-1 VBS model while in the other we obtain a new anisotropic generalisation of the spin-½ Majumdar-Ghosh model.

Exact Antiferromagnetic Ground States of Quantum Spin Chains

1989 ◽  
Vol 10 (7) ◽  
pp. 633-637 ◽  
Author(s):  
M Fannes ◽  
B Nachtergaele ◽  
R. F Werner
Keyword(s):  
Ground States ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains

scholarly journals Long-distance entanglement in Motzkin and Fredkin spin chains

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Luca Dell'Anna
Keyword(s):  
Mutual Information ◽  
Entanglement Entropy ◽  
Ground States ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Long Distance ◽  
Half Integer ◽  
Quantum Mutual Information

We derive some entanglement properties of the ground states for two classes of quantum spin chains described by the Fredkin model, for half-integer spins, and the Motzkin model, for integer ones. Since the ground states of the two models are known analytically, we can calculate exactly the entanglement entropy, the negativity and the quantum mutual information. We show, in particular, that these systems exhibit long-distance entanglement, namely two disjoint regions of the chains remain entangled even when their separation is sent to infinity, i.e. these systems are not affected by decoherence. This strongly entangled behavior, Finally, we show that this behavior involves disjoint segments located both at the edges and in the bulk of the chains.

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