Constructing soluble quantum spin models - Department of Physics ...
Constructing soluble quantum spin models - Department of Physics ...
Constructing soluble quantum spin models - Department of Physics ...
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H.Y. Shik et al. / Nuclear <strong>Physics</strong> B 666 [FS] (2003) 337–360 347<br />
+ 2 ˜<br />
+ 2J ‖ 7<br />
K−2,L−2,M−1<br />
∑<br />
J 7<br />
k,l,m=1<br />
K−2,L−2,M<br />
∑<br />
k,l,m=1<br />
S ′ k,l,m · (S k+2,l,m+1 + S k,l+2,m+1 )<br />
+ S k,l,m+1 · (S ′ k+2,l,m + S′ k,l+2,m )<br />
S k,l,m · (S k+2,l+1,m + S k+1,l+2,m )<br />
+ S ′ k,l,m · (S′ k+2,l+1,m + S′ k+1,l+2,m )<br />
+ S k,l+2,m · (S k+1,l,m + S k+2,l+1,m )<br />
+ S ′ k,l+2,m · (S′ k+1,l,m + S′ k+2,l+1,m )<br />
K−1,L−1,M−1<br />
∑<br />
+ 2J 8 S k,l,m · (S k+1,l,m+1 + S k,l+1,m+1 )<br />
k,l,m=1<br />
+ S ′ k,l,m · (S′ k+1,l,m+1 + S′ k,l+1,m+1 )<br />
+ S k,l,m+1 · (S k+1,l,m + S k,l+1,m )<br />
+ S ′ k,l,m+1 · (S′ k+1,l,m + S′ k,l+1,m )<br />
K−1,L−1,M−1<br />
∑<br />
+ 2J 9 S k,l,m · S k+1,l+1,m+1 + S k+1,l,m · S k,l+1,m+1<br />
k,l,m=1<br />
+ S k+1,l+1,m · S k,l,m+1 + S k,l+1,m · S k+1,l,m+1<br />
+ S ′ k,l,m · S′ k+1,l+1,m+1 + S′ k+1,l,m · S′ k,l+1,m+1<br />
K−2,L−1,M−1<br />
∑<br />
+ 2J 10<br />
+ 2 ˜<br />
k,l,m=1<br />
K−2,L−1,M−1<br />
∑<br />
J 10<br />
k,l,m=1<br />
K−2,L−2,M<br />
∑<br />
+ 2J 11<br />
+ 2J ‖ 11<br />
k,l,m=1<br />
K−2,L−2,M<br />
∑<br />
k,l,m=1<br />
+ S ′ k+1,l+1,m · S′ k,l,m+1 + S′ k,l+1,m · S′ k+1,l,m+1<br />
S k,l,m · S ′ k+2,l+1,m + S k+2,l,m · S ′ k,l+1,m<br />
+ S k+2,l+1,m · S ′ k,l,m + S k,l+1,m · S ′ k+2,l,m<br />
S ′ k,l,m · S k+2,l+1,m+1 + S ′ k+2,l,m · S k,l+1,m+1<br />
+ S ′ k+2,l+1,m · S k,l,m+1 + S ′ k,l+1,m · S k+2,l,m+1<br />
S k,l,m · (S k+2,l,m+1 + S k,l+2,m+1 )<br />
+ S ′ k,l,m · (S′ k+2,l,m+1 + S′ k,l+2,m+1 )<br />
+ S k,l,m+1 · (S k+2,l,m + S k,l+2,m )<br />
+ S ′ k,l,m+1 · (S′ k+2,l,m + S′ k,l+2,m )<br />
S k,l,m · S k+2,l+2,m + S ′ k,l,m · S′ k+2,l+2,m<br />
+ S k,l+2,m · S k+2,l,m + S ′ k,l+2,m · S′ k+2,l,m .<br />
(42)