Constructing soluble quantum spin models - Department of Physics ...

More documents

Recommendations

Info

352 H.Y. Shik et al. / Nuclear Physics B 666 [FS] (2003) 337–360 Fig. 6. The three-dimensional model constructed by conditions 2J 2 = J 3 + J 4 and 2 ˜ J 5 = J ‖ 3 + J ‖ 4 . 5.3. Three-dimensional model I: 2 ˜ J 5 = J ‖ 3 + J ‖ 4 Actually, coupling J˜ 5 could take the role of J 5 to cancel the effects of J ‖ 3 and J ‖ 4 on the dimers. So previous condition is modified to J 5 = 0,J 9 = 0, 2J˜ 5 = J ‖ 3 + J ‖ 4 .Thisisa simple three-dimensional model as shown in Fig. 6. 5.4. Three-dimensional model II: J ‖ 6 = ˜ J 7 Similarly to Section 5.2, the role of J 7 in Section 5.3 can be replaced by J˜ 7 with J 11 set to zero, results in a soluble 3D model as shown in Fig. 7. Note that we use open boundary conditions so there exist no J ‖ 6 on the bottom and top layers. 5.5. Three-dimensional model III: ˜ J 1 = 2J 6 The model is shown in Fig. 8, which can be considered as an extension of the nestedladder model discussed in Section 4. A generalization of this case is that if there exists coupling J a , which connects S k,l,m and S ′ k,l,m+1 , then the condition for the completely dimerized state to be an eigenstate of the Hamiltonian would be J a + J˜ 1 = 2J 6 .
H.Y. Shik et al. / Nuclear Physics B 666 [FS] (2003) 337–360 353 Fig. 7. The three-dimensional model constructed by conditions 2J 2 = J 3 + J 4 and J ‖ 6 = ˜ J 7 . Fig. 8. The three-dimensional model constructed by conditions 2J 2 = J 3 + J 4 and ˜ J 1 = 2J 6 . 5.6. More three-dimensional models In fact, each independent set of conditions as specified in Eq. (43) will lead to a threedimensional soluble model in which the completely dimerized state is an eigenstate of
Page 1 and 2: Nuclear Physics B 666 [FS] (2003) 3
Page 3 and 4: H.Y. Shik et al. / Nuclear Physics
Page 15: H.Y. Shik et al. / Nuclear Physics

Constructing soluble quantum spin models - Department of Physics ...

Create successful ePaper yourself

Delete template?

Save as template?