- #1
Petar Mali
- 290
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[tex]\hat{H}=\hat{H}_0+S\sum_{i,j}I_{i,j}(\hat{a}_i\hat{b}_j+\hat{a}_i^+\hat{b}_j^++\hat{b}
^+_j\hat{b}_j+\hat{a}
^+_i\hat{a}_i)-\sum_{i,j}I_{i,j}[\frac{1}{2}(\hat{a}_i\hat{b}
^+_j\hat{b}_j\hat{b}_j+\hat{a}^+_i\hat{a}^+_i\hat{a}_i\hat{b}
^+_j)+\hat{a}
^+_i\hat{a}_i\hat{b}
^+_j\hat{b}_j][/tex]
[tex]\hat{a}_i,\hat{a}_i^+,\hat{b}_j,\hat{b}_j^+[/tex] - bose operators
SCSW - theory
[tex]\hat{H}=\hat{H}_0+\hat{H}_2+\hat{H}_4^{SC}[/tex]
[tex]\hat{H}_2=S\sum_{i,j}I_{i,j}(\hat{a}_i\hat{b}_j+\hat{a}_i^+\hat{b}_j^++\hat{b}
^+_j\hat{b}_j+\hat{a}
^+_i\hat{a}_i)[/tex]
How is [tex]\hat{H}^{SC}_{4}[/tex] defined?
Term[tex]-\sum_{i,j}I_{i,j}[\frac{1}{2}(\hat{a}_i\hat{b}
^+_j\hat{b}_j\hat{b}_j+\hat{a}^+_i\hat{a}^+_i\hat{a}_i\hat{b}
^+_j)+\hat{a}
^+_i\hat{a}_i\hat{b}
^+_j\hat{b}_j][/tex] represent magnon - magnon interractions.
^+_j\hat{b}_j+\hat{a}
^+_i\hat{a}_i)-\sum_{i,j}I_{i,j}[\frac{1}{2}(\hat{a}_i\hat{b}
^+_j\hat{b}_j\hat{b}_j+\hat{a}^+_i\hat{a}^+_i\hat{a}_i\hat{b}
^+_j)+\hat{a}
^+_i\hat{a}_i\hat{b}
^+_j\hat{b}_j][/tex]
[tex]\hat{a}_i,\hat{a}_i^+,\hat{b}_j,\hat{b}_j^+[/tex] - bose operators
SCSW - theory
[tex]\hat{H}=\hat{H}_0+\hat{H}_2+\hat{H}_4^{SC}[/tex]
[tex]\hat{H}_2=S\sum_{i,j}I_{i,j}(\hat{a}_i\hat{b}_j+\hat{a}_i^+\hat{b}_j^++\hat{b}
^+_j\hat{b}_j+\hat{a}
^+_i\hat{a}_i)[/tex]
How is [tex]\hat{H}^{SC}_{4}[/tex] defined?
Term[tex]-\sum_{i,j}I_{i,j}[\frac{1}{2}(\hat{a}_i\hat{b}
^+_j\hat{b}_j\hat{b}_j+\hat{a}^+_i\hat{a}^+_i\hat{a}_i\hat{b}
^+_j)+\hat{a}
^+_i\hat{a}_i\hat{b}
^+_j\hat{b}_j][/tex] represent magnon - magnon interractions.
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