Theoretical study of one-dimensional quantum spin sustems : q in which two kinds of spins are arranged alternatively

We have investigated both analytically and numerically the ground-state and thermodynamic properties of the quantum mixed spin-1/2-1-1 chain described by the Hamiltonian H=ΣI D31N/4(/)l=1个D 3(J-D21-D 2-S-D4→D 4-D 24 l-3 D 2·S D 4→D 4 D 24 l-2 D 2+J I D 22 D D 2 s D 4 D 4 D 2 D 2 D 2D 4→D 4 D 24 l-1 D 2+J D 23 D 2 S D 4→I D 4 D 24 l-1 D 2/S D 4→D 4 D 24 l D 2+J D 22 I D 2 S D 4 4→D 4 D 4 I D 4→D 4 I D 4→D 4 D 24 l+1 D 2)，Where two S=1/2 spins(s D 4→D 4 I D 24 l-3 D 2 and s D 4→I D 4 D 24 l-2 D 2)and two S=1 spins(S D 4→D 4 D 24 l D 4→D 4 D 24 l D 2 are arrayed alternatively.In several limiting cases of J I D 21 D 2，J I D 22 D 2，and J I D 23 d 2，d d 2，d 2 d 2，D 2 d 2，D 2 d 2，D 2In these cases，of the massless lines where the energy gap vanishes.Guided by these results，we have performed a density-matrix renormalization-group calculation to determine in detail the ground-state phase diagram on t…More he J I D 21 I D 2 versus J I D 22 I D 2 plane with J I D 23 I D 2=1.0。From the gapless points of the singlet-triplet energy gap，five boundary lines have been determined，which divide the phase diagram into six regions。In three regions the ground states with the Haldane-phase character appear，while in the remaining three regions those with the dimer character appear。We have also presented a characterization of the phases concerning how the ground state in each phase is represented in the framework of the valence-bond-solid(VBS)picture.Making use of the matrix-product wave function，we have classified the VBS pictures and interpreted the ground-state phase diagram in terms of symmetries schematically related to the VBS pictures.We have investigated the ground-state nearest-neighboring two-spin correlation functions and a kind of string order parameters，by which we have confirmed the validity of the characterization.Furthermore，we have carried out a quantum Monte Carlo calculation which takes the global flips along the Trotter direction into account to elucidate the temperature dependences of the specific heat and the magnetic susceptibility。In particular，we have found that the specific heat per unit cell versus temperature curve for J I D22文件D2=5.0 with J I D 21文件D2=J I D 23文件D2=1.0 has a double peak.Less：Less

We have investigated both analytically and numerically the ground-state and thermodynamic properties of the quantum mixed spin-1/2-1/2-1-1 chain described by the Hamiltonian H = ΣィイD31N/4(/)l=1ィエD3(JィイD21ィエD2・SィイD4→ィエD4ィイD24l-3ィエD2・sィイD4→ィエD4ィイD24l-2ィエD2 + JィイD22ィエD2 sィイD4→ィエD4ィイD24l-2ィエD2・SィイD4→ィエD4ィイD24l-1ィエD2 + JィイD23ィエD2 SィイD4→ィエD4ィイD24l-1ィエD2・SィイD4→ィエD4ィイD24lィエD2 + JィイD22ィエD2 SィイD4→ィエD4ィイD24lィエD2・sィイD4→ィエD4ィイD24l+1ィエD2), where two S = 1/2 spins (sィイD4→ィエD4ィイD24l-3ィエD2 and sィイD4→ィエD4ィイD24l-2ィエD2) and two S = 1 spins (SィイD4→ィエD4ィイD24l-1ィエD2 and ィイD4→ィエD4ィイD24lィエD2 are arrayed alternatively.In several limiting cases of JィイD21ィエD2, JィイD22ィエD2, and JィイD23ィエD2 we have applied the Wigner-Eckart theorem and carried out a perturbation calculation to examine the behaviors, in these cases, of the massless lines where the energy gap vanishes. Guided by these results, we have performed a density-matrix renormalization-group calculation to determine in detail the ground-state phase diagram on t … More he JィイD21ィエD2 versus JィイD22ィエD2 plane with JィイD23ィエD2 = 1.0. From the gapless points of the singlet-triplet energy gap, five boundary lines have been determined, which divide the phase diagram into six regions. In three regions the ground states with the Haldane-phase character appear, while in the remaining three regions those with the dimer character appear. We have also presented a characterization of the phases concerning how the ground state in each phase is represented in the framework of the valence-bond-solid (VBS) picture. Making use of the matrix-product wave function, we have classified the VBS pictures and interpreted the ground-state phase diagram in terms of symmetries schematically related to the VBS pictures. We have investigated the ground-state nearest-neighboring two-spin correlation functions and a kind of string order parameters, by which we have confirmed the validity of the characterization.Furthermore, we have carried out a quantum Monte Carlo calculation which takes the global flips along the Trotter direction into account to elucidate the temperature dependences of the specific heat and the magnetic susceptibility. In particular, we have found that the specific heat per unit cell versus temperature curve for JィイD22ィエD2 = 5.0 with JィイD21ィエD2 = JィイD23ィエD2 = 1.0 has a double peak. Less