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.
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.
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 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.
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 study the ground-state phase diagram of the quantum spin-2 XXZ chain in the presence of on-site anisotropy using a matrix-product state based infinite-system density matrix renormalization group (iDMRG) algorithm. One of the interests in this system is in connecting the highly quantum-mechanical spin-1 phase diagram with the classical $S=\ensuremath{\infty}$ phase diagram. Several of the recent advances within DMRG make it possible to perform a detailed analysis of the whole phase diagram. We consider different types of on-site anisotropies, which allows us to establish the validity of the following statements: (1) the spin-2 model can be tuned into a phase, which is equivalent to the ``topologically nontrivial'' spin-1 Haldane phase, and (2) the spin-2 Haldane phase at the isotropic Heisenberg point is adiabatically connected to the ``trivial'' large-
D phase, with a continuous change of the Hamiltonian parameters. Furthermore, we study the spin-3 XXZ chain to help explain the development of the classical phase diagram. We present details on how to use the iDMRG method to map out the phase diagram and include an extensive discussion of the numerical methods.