Haldane, Large-D, and Intermediate-DStates in anS= 2 Quantum Spin Chain with On-Site andXXZAnisotropies

Abstract

Using mainly numerical methods, we investigate the ground-state phase diagram of the S = 2 quantum spin chain described by H = j (S Quantum spin chain systems have been attracting increasing attention in recent years because they provide rich physics even when models are rather simple. The most well-known example may be the existence of the Haldane phase 1, 2) in integer spin chain systems only with isotropic nearest-neighbor (nn) interactions.In this study, using mainly numerical methods, we explore the ground-state phase diagram of the S = 2 quantum spin chain described by the Hamiltonianwhere S α j (α = x, y, z) is the α-component of the S = 2 operator at the j-th site, and ∆ and D are, respectively, the XXZ anisotropy parameter of the nn interactions and the on-site anisotropy parameter. Hereafter, we denote the total number of spins in the system by N , assumed to be even, and the z component of the total spin by M = j S z j . The ground-state phase diagram on the ∆-D plane of the same Hamiltonian in the S = 1 case was discussed by Schulz 3) and den Nijs and Rommels, 4) and numerically determined by Chen et al. 5) In the present S = 2 case, Schulz 3) discussed the ground-state phase diagram with six phases obtained by the bosonization method; the phases are, in our terminology, the ferromagnetic (FM) phase, the Néel phase, the XY 1 phase, the XY 4 phase, the Haldane phase and the large-D (LD) phase. The XY 1 state is characterized by the power decay of * E-mail address: tone0115@vivid.ocn.ne.jp Figs. 1(a) and (c), respectively. About twenty years ago, Oshikawa 6) predicted, in S ≥ 2 integer quantum spin cases, the existence of the intermediate-D (ID) phase, the valence bond picture of which is depicted in Fig. 1(b). Figure 2(a) is an interpretation of Oshikawa's prediction by Aschauer and Schollwöck 7) in the S = 2 case. On the other hand, carrying out the density-matrix renormalization-group (DMRG) calculation, Schollwöck et al. 8,9) and Aschauer and Schollwöck 7) proposed the phase diagram in Fig. 2(b) and concluded the absence of

Symmetry protection of topological phases in one-dimensional quantum spin systems

“…A similar adiabatic connection between the S = 2 AKLT state and a trivial state is suggested recently in the analysis of finite-length S = 2 chains with both exchange and single-ion anisotropy. 40 Even if the full SU(2) invariance is maintained along the path, we have demonstrated that an even-S AKLT state is adiabatically connectable to a trivial dimerized state with broken translational symmetry.…”

Antiferromagnetic ordering in MnF(salen)

“…[20][21][22][23][24][25][26][27] Recently, a new S = 2 linear-chain system, MnF(salen), salen = H 14 C 16 N 2 O 2 , was synthesized, and the low-field, high-temperature magnetic properties were fit with J/k B ≈ 46 K, while no evidence of a magnetic transition was detected down to 1.8 K.…”

Long-range magnetic order and interchain interactions in theS=2chain systemMnCl3(bpy)

“…Magnetic chains composed of spin S = 2 ions have received considerable theoretical and numerical attention [1][2][3][4][5][6][7][8] due to their unique predicted behavior. Even-and odd-integer spin chains are distinct, with the latter in a symmetry-protected topological phase [3,9].…”