scholarly journals A classification of pure states on quantum spin chains satisfying the split property with on-site finite group symmetries

2021 ◽  
Vol 8 (2) ◽  
pp. 39-65
Author(s):  
Yoshiko Ogata
Keyword(s):  
Finite Group ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Split Property ◽  
Pure States ◽  
Group Symmetries

scholarly journals ON HAAG DUALITY FOR PURE STATES OF QUANTUM SPIN CHAINS

2008 ◽  
Vol 20 (06) ◽  
pp. 707-724 ◽  
Author(s):  
M. KEYL ◽  
TAKU MATSUI ◽  
D. SCHLINGEMANN ◽  
R. F. WERNER
Keyword(s):  
Von Neumann Algebra ◽  
Quantum Spin ◽  
Spin Chains ◽  
Type I ◽  
Quantum Spin Chains ◽  
Haag Duality ◽  
Von Neumann ◽  
Infinite Intervals ◽  
Pure States

In this note, we consider quantum spin chains and their translationally invariant pure states. We prove Haag duality for quasilocal observables localized in semi-infinite intervals (-∞ , 0] and [1, ∞) when the von Neumann algebra generated by observables localized in [0, ∞) is non-type I.

Abundance of translation invariant pure states on quantum spin chains

1992 ◽  
Vol 25 (3) ◽  
pp. 249-258 ◽  
Author(s):  
M. Fannes ◽  
B. Nachtergaele ◽  
R. F. Werner
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Translation Invariant ◽  
Pure States

scholarly journals BOUNDEDNESS OF ENTANGLEMENT ENTROPY AND SPLIT PROPERTY OF QUANTUM SPIN CHAINS

2013 ◽  
Vol 25 (09) ◽  
pp. 1350017 ◽  
Author(s):  
TAKU MATSUI
Keyword(s):  
Spectral Gap ◽  
Entanglement Entropy ◽  
Quantum Spin ◽  
Spin Systems ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Quantum Spin Systems ◽  
One Dimensional ◽  
Split Property ◽  
Left And Right

We show that boundedness of entanglement entropy for pure states of bipartite quantum spin systems implies split property of subsystems. As a corollary, in one-dimensional quantum spin chains, we show that the split property with respect to left and right semi-infinite subsystems is valid for the translationally invariant pure ground states with spectral gap.

Solvable nineteen-vertex models and quantum spin chains of spin one

1994 ◽  
Vol 4 (8) ◽  
pp. 1151-1159 ◽  
Author(s):  
Makoto Idzumi ◽  
Tetsuji Tokihiro ◽  
Masao Arai
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Vertex Models
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