Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Conference Series

Ground-state phase diagram of S = 2 quantum spin chain with the XXZ and on-site anisotropies

Kiyomi Okamoto, Takashi Tonegawa, Hiroki Nakano, Tôru Sakai, K. Nomura, Makoto Kaburagi

Published Jul 20, 2011• 11 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/302/1/012014

Related papers

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

Takashi Tonegawa, Kiyomi Okamoto, Hiroki Nakano +3 more

Using mainly numerical methods, we investigate the ground-state phase diagram of the S=2 quantum spin chain described by $H = \sum_j (S_j^x S_{j+1}^x + S_j^y S_{j+1}^y + ΔS_j^z S_{j+1}^z) + D \sum_j (S_j^z)^2$, where $Δ$ denotes the $XXZ$ anisotropy parameter of the nearest-neighbor interactions and $D$ the on-site anisotropy parameter. We restrict ourselves to the case with $Δ\ge 0$ and $D \ge 0$ 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.

arXiv:1011.6568•Journal of the Physical Society of Japan•Apr 12, 2011•49 citations

How to distinguish the Haldane/Large-Dstate and the intermediate-Dstate in anS= 2 quantum spin chain with theXXZand on-site anisotropies

Kiyomi Okamoto, Takashi Tonegawa, Hiroki Nakano +3 more

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.

arXiv:1101.2799•Journal of Physics Conference Series•Sep 28, 2011•18 citations

Edge Modes in the Intermediate-D and Large-D Phases of the S = 2 Quantum Spin Chain with XXZ and On-Site Anisotropies

Kiyomi Okamoto, Takashi Tonegawa, Tôru Sakai +1 more

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.

arXiv:1310.3385•International Conference on Strongly Correlated Electron Systems (SCES)•Jun 16, 2014•7 citations

Ground-State Phase Diagram of an Anisotropic S = 1 Ferromagnetic–Antiferromagnetic Bond-Alternating Chain

Kiyomi Okamoto, Takashi Tonegawa, Makoto Kaburagi +1 more

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$1, the large-$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.

arXiv:1910.02456•International Conference on Strongly Correlated Electron Systems (SCES)•Mar 18, 2020•0 citations

Ground-State Phase Diagram of the Bond-Alternating S = 2 Quantum Spin Chain with the XXZ and On-Site Anisotropies — Symmetry Protected Topological Phase versus Trivial Phase —

Kiyomi Okamoto, Takashi Tonegawa, Tôru Sakai

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 $D_2 \sum_j (S_j^z)^2$ term, we consider the $D_4 \sum_j (S_j^z)^4$ 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.

arXiv:1604.00452•Journal of the Physical Society of Japan•May 23, 2016•8 citations

Phase diagram of the anisotropic spin-2 XXZ model: Infinite-system density matrix renormalization group study

Jonas A. Kjäll, Michael P. Zaletel, Roger S. K. Mong +2 more

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.

arXiv:1212.6255•Physical Review B•Jun 6, 2013•137 citations
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)2H = \sum_j (S_j^x S_{j+1}^x + S_j^y S_{j+1}^y + ΔS_j^z S_{j+1}^z) + D \sum_j (S_j^z)^2H=∑j​(Sjx​Sj+1x​+Sjy​Sj+1y​+ΔSjz​Sj+1z​)+D∑j​(Sjz​)2, where ΔΔΔ denotes the XXZXXZXXZ anisotropy parameter of the nearest-neighbor interactions and DDD the on-site anisotropy parameter. We restrict ourselves to the case with Δ≥0Δ\ge 0Δ≥0 and D≥0D \ge 0D≥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 ΔΔΔ-DDD plane consists of four phases; the XY 1 phase, the Haldane/large-DDD phase, the intermediate-DDD phase and the Néel phase. The remarkable natures of the phase diagram are: (1) the Haldane state and the large-DDD state belong to the same phase; (2) there exists the intermediate-DDD phase which was predicted by Oshikawa in 1992; (3) the shape of the phase diagram on the ΔΔΔ-DDD plane is different from that believed so far. We note that this is the first report of the observation of the intermediate-DDD 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.
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=1S=1S=1 ferromagnetic-antiferromagnetic bond-alternating chain with the XXZXXZXXZ 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 XXZXXZXXZ 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 $XY1,thelarge−1, the large-1,thelarge−D$ (LD), the intermediate-DDD (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 XXZXXZXXZ 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=2S=2S=2 quantum spin chain with the XXZXXZXXZ and on-site anisotropies. For the on-site anisotropies, in addition to the popular D2∑j(Sjz)2D_2 \sum_j (S_j^z)^2D2​∑j​(Sjz​)2 term, we consider the D4∑j(Sjz)4D_4 \sum_j (S_j^z)^4D4​∑j​(Sjz​)4 term. Mainly we use the exact diagonalization and the level spectroscopy analysis. We show that the Haldane state, large-DDD 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-DDD state and the Dimer1 state belong to the same symmetry protected topological phase.
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-DDD 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.