We numerically investigate the ground-state phase diagram of an S = 2 quantum spin chain with the XXZ and on-site anisotropies described by = Σ j ( S j x S j + 1 x + S j y S j + 1 y + Δ S j z S j+1 z ) + D Σ j ( S j z ) 2 , where Δ denotes the XXZ anisotropy parameter of the nearest-neighbor interactions and D the on-site anisotropy parameter. We restrict ourselves to the Δ > 0 and D > 0 case for simplicity. Our main purpose is to obtain the definite conclusion whether there exists or not the intermediate- D (ID) phase, which was proposed by Oshikawa in 1992 and has been believed to be absent since the DMRG studies in the latter half of 1990's. In the phase diagram with Δ > 0 and D > 0 there appear the XY state, the Haldane state, the ID state, the large- D (LD) state and the Néel state. In the analysis of the numerical data it is important to distinguish three gapped states; the Haldane state, the ID state and the LD state. We give a physical and intuitive explanation for our level spectroscopy method how to distinguish these three phases.
By use of mainly numerical methods, we investigate the ground-state phase diagram of an S = 2 quantum spin chain with the XXZ and on-site anisotropies described by = Σ j ( S j x S j +1 x + S y j S y j +1 + Δ S z j S z j +1 + D Σ j ( S z j ) 2 , where Δ denotes the XXZ anisotropy parameter of the nearest-neighbor interactions and D the on-site anisotropy parameter. In the phase diagram with Δ > 0 and D > 0 there appear the XY phase, the Haldane/large- D (LD) phase, the intermediate- D (ID) phase, and the Néel phase. Among them the ID phase was proposed by Oshikawa in 1992 and has been considered to be absent since the DMRG studies in the latter half of 1990's. And also, the Haldane state and the LD state belong to the same phase, which should be named Haldane/LD phase.
Using mainly numerical methods, we investigate the ground-state phase diagram of the S=2 quantum spin chain described by
H=∑j(SjxSj+1x+SjySj+1y+ΔSjzSj+1z)+D∑j(Sjz)2, where
Δ denotes the
XXZ anisotropy parameter of the nearest-neighbor interactions and
D the on-site anisotropy parameter. We restrict ourselves to the case with
Δ≥0 and
D≥0 for simplicity. Each of the phase boundary lines is determined by the level spectroscopy or the phenomenological renormalization analysis of numerical results of exact-diagonalization calculations. The resulting phase diagram on the
Δ-
D plane consists of four phases; the XY 1 phase, the Haldane/large-
D phase, the intermediate-
D phase and the Néel phase. The remarkable natures of the phase diagram are: (1) the Haldane state and the large-
D state belong to the same phase; (2) there exists the intermediate-
D phase which was predicted by Oshikawa in 1992; (3) the shape of the phase diagram on the
Δ-
D plane is different from that believed so far. We note that this is the first report of the observation of the intermediate-
D phase.
We investigate the edge modes at T=0 in the intermediate-D (ID) phase and the large-D (LD) phase of the S=2 quantum spin chain with the XXZ anisotropy and the generalized on-site anisotropies by use of the DMRG. There exists a gapless edge mode in the ID phase, while no gapless edge mode in the LD phase. These results are consistent with the physical pictures of these phases. We also show the ground-state phase diagrams obtained by use of the exact diagonalization and the level spectroscopy analysis.
By using mainly numerical methods, we investigate the ground-state phase diagram (GSPD) of an
S=1 ferromagnetic-antiferromagnetic bond-alternating chain with the
XXZ and the on-site anisotropies. This system can be mapped onto an anisotropic spin-2 chain when the ferromagnetic interaction is much stronger than the antiferromagnetic interaction. Since there are many quantum parameters in this system, we numerically obtained the GSPD on the plane of the magnitude of the antiferromagnetic coupling versus its
XXZ anisotropy, by use of the exact diagonalization, the level spectroscopy as well as the phenomenological renormalization group. The obtained GSPD consists of six phases. They are the $XY
1,thelarge−D$ (LD), the intermediate-
D (ID), the Haldane (H), the spin-1 singlet dimer (SD), and the Néel phases. Among them, the LD, the H, and the SD phases are the trivial phases, while the ID phase is the symmetry-protected topological phase. The former three are smoothly connected without any quantum phase transitions. It is also emphasized that the ID phase appears in a wider region compared with the case of the GSPD of the anisotropic spin-2 chain with the
XXZ and the on-site anisotropies. We also compare the obtained GSPD with the result of the perturbation theory.
We investigate the ground-state phase diagram of the bond-alternating
S=2 quantum spin chain with the
XXZ and on-site anisotropies. For the on-site anisotropies, in addition to the popular
D2∑j(Sjz)2 term, we consider the
D4∑j(Sjz)4 term. Mainly we use the exact diagonalization and the level spectroscopy analysis. We show that the Haldane state, large-
D state and the Dimer2 state belong to the same trivial phase, by finding the existence of adiabatic paths directly connecting these states without the quantum phase transition. Similarly, we show that the intermediate-
D state and the Dimer1 state belong to the same symmetry protected topological phase.
We investigate the inversion phenomenon between the XXZ anisotropies of the Hamiltonian and the wave function in quantum spin chains, focusing mainly on the S = 1/2 trimerized XXZ model with the next-nearest-neighbor interactions. We have obtained the ground-state phase diagram by use of the degenerate perturbation theory and the level spectroscopy analysis of the numerical data calculated by the Lanczös method. In some parameter regions, the spin-fluid phase is realized for the Ising-like anisotropy, and the Néel phase for the XY-like anisotropy, against the ordinary situation.