Physical review. B, Condensed matter

Reply to "Comment on `Ground-state properties of a spin-1 antiferromagnetic chain' "

Robert S. Botet, Rémi Jullien, M. Kolb

Published May 1, 1984• 14 citations

Abstract

We contrast, on the same figure, our phenomenological renormalization-group results on the $S=1$ Heisenberg-Ising antiferromagnetic chain with results that we have recently obtained for $S=\frac{1}{2}$ and $S=\frac{3}{2}$. The different behaviors of integer- and half-integer-spin chains are revealed very clearly. This confirms the conclusion of our Communication.

DOI: 10.1103/physrevb.29.5222

Related papers

Comment on "Ground-state properties of a spin-1 antiferromagnetic chain"

Jill C. Bonner, Gerhard H. Muller

Physical review. B, Condensed matterMay 1, 198480 citations

Comment on "Ground-state properties of a spin-1 antiferromagnetic chain"

Daniel Charles Mattis

Physical review. B, Condensed matterApr 1, 19854 citations

Comment on 'Ground-State Phase Diagram of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chains with Anisotropy'

清美岡本, Kiyomi Okamoto

Jan 1, 19930 citations

Comparison of ground state properties for odd half-integer and integer spin antiferromagnetic Heisenberg chains

M. Kolb, Robert S. Botet, Rémi Jullien

Journal of Physics A Mathematical and GeneralDec 1, 198375 citations

Magnetic properties ofJ–J–J′ quantum Heisenberg chains with spinS= 1/2, 1, 3/2 and 2 in a magnetic field

Bo Gu, Gang Su, Song Gao

arXiv:cond-mat/0508685Journal of Physics Condensed MatterSep 9, 200527 citations

Edge states in open antiferromagnetic Heisenberg chains

Shaojin Qin, Tai Kai Ng, Zhao-Bin Su

arXiv:cond-mat/9502047Physical review. B, Condensed matterNov 1, 199553 citations

Physical review. B, Condensed matter

Reply to "Comment on `Ground-state properties of a spin-1 antiferromagnetic chain' "

Robert S. Botet, Rémi Jullien, M. Kolb

Published May 1, 1984• 14 citations

Publisher

Abstract

We contrast, on the same figure, our phenomenological renormalization-group results on the

S=1

Heisenberg-Ising antiferromagnetic chain with results that we have recently obtained for

S=\frac{1}{2}

and

S=\frac{3}{2}

. The different behaviors of integer- and half-integer-spin chains are revealed very clearly. This confirms the conclusion of our Communication.

DOI: 10.1103/physrevb.29.5222

Related papers

Comment on "Ground-state properties of a spin-1 antiferromagnetic chain"

Jill C. Bonner, Gerhard H. Muller

Botet and Jullien [Phys. Rev. B 27, 613 (1983)] have conducted a finite-chain scaling analysis on the spin-1 antiferromagnetic Heisenberg-Ising chain. They claim that the ground-state properties are completely different from the case of spin $\frac{1}{2}$ . Using finite-size scaling techniques, they conclude that between the $\mathrm{XY}$ gapless phase and the doublet-ground-state N\'eel phase, a new phase appears in an extended anisotropy range. This phase, which encompasses the isotropic Heisenberg model, is characterized by a nonmagnetic singlet ground state and a nonzero excitation-energy gap. We perform a similar finite-chain scaling analysis on the spin- $\frac{1}{2}$ antiferromagnetic Heisenberg-Ising chain and obtain strikingly similar results. Since the spin- $\frac{1}{4}$ system is known rigorously not to exhibit the type of behavior proposed by Botet and Jullien, their analysis is open to doubt. The possibility arises that a strong singularity at the Heisenberg point for spin 1 (similar to the essential singularity for spin $\frac{1}{2}$ ) may be giving rise to misleading results. The $T=0$ phase behavior of the spin-1 Heisenberg-Ising antiferromagnetic chain, therefore, remains in question and specific additional numerical studies are proposed to clarify the matter.Botet and Jullien [Phys. Rev. B 27, 613 (1983)] have conducted a finite-chain scaling analysis on the spin-1 antiferromagnetic Heisenberg-Ising chain. They claim that the ground-state properties are completely different from the case of spin $\frac{1}{2}$. Using finite-size scaling techniques, they conclude that between the $\mathrm{XY}$ gapless phase and the doublet-ground-state N\'eel phase, a new phase appears in an extended anisotropy range. This phase, which encompasses the isotropic Heisenberg model, is characterized by a nonmagnetic singlet ground state and a nonzero excitation-energy gap. We perform a similar finite-chain scaling analysis on the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg-Ising chain and obtain strikingly similar results. Since the spin-$\frac{1}{4}$ system is known rigorously not to exhibit the type of behavior proposed by Botet and Jullien, their analysis is open to doubt. The possibility arises that a strong singularity at the Heisenberg point for spin 1 (similar to the essential singularity for spin $\frac{1}{2}$) may be giving rise to misleading results. The $T=0$ phase behavior of the spin-1 Heisenberg-Ising antiferromagnetic chain, therefore, remains in question and specific additional numerical studies are proposed to clarify the matter.

Physical review. B, Condensed matterMay 1, 198480 citations

Comment on "Ground-state properties of a spin-1 antiferromagnetic chain"

Daniel Charles Mattis

Botet and Jullien [Phys. Rev. B 27, 613 (1983)] and Botet, Jullien, and Kolb [Phys. Rev. B 28, 3914 (1983)] performed a finite-size scaling analysis of the spin-1 antiferromagnetic Heisenberg-Ising chain. Their work was criticized by Bonner and M\"uller [Phys. Rev. B 29, 5216 (1984)] on the grounds that a similar analysis for spin \textonehalf{} yields misleading results. In the present work, we show that the plane-rotator version of spin-1 chain has some features similar to that obtained by Botet et al., although, unfortunately, our model can be solved analytically only over a restricted set of the parameters, and thus does not unambiguously confirm their results. The need for further studies is emphasized.Botet and Jullien [Phys. Rev. B 27, 613 (1983)] and Botet, Jullien, and Kolb [Phys. Rev. B 28, 3914 (1983)] performed a finite-size scaling analysis of the spin-1 antiferromagnetic Heisenberg-Ising chain. Their work was criticized by Bonner and M\"uller [Phys. Rev. B 29, 5216 (1984)] on the grounds that a similar analysis for spin \textonehalf{} yields misleading results. In the present work, we show that the plane-rotator version of spin-1 chain has some features similar to that obtained by Botet et al., although, unfortunately, our model can be solved analytically only over a restricted set of the parameters, and thus does not unambiguously confirm their results. The need for further studies is emphasized.

Physical review. B, Condensed matterApr 1, 19854 citations

Comment on 'Ground-State Phase Diagram of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chains with Anisotropy'

清美岡本, Kiyomi Okamoto

Jan 1, 19930 citations

Comparison of ground state properties for odd half-integer and integer spin antiferromagnetic Heisenberg chains

M. Kolb, Robert S. Botet, Rémi Jullien

Ground state properties of finite anisotropic antiferromagnetic Heisenberg chains are studied for odd half-integer spins S= 1 / 2 , 3 / 2 ... as well as integer spins S=1, 2 .... Finite size scaling analysis of the results clearly distinguishes the half-integer (S= 1 / 2 , 3 / 2 ) from the integer (S=1) spin situation. It gives strong support to a recent conjecture which postulates that the T=0 phase structure is very different in the two cases. According to this idea there exists a new phase between the planar and the antiferromagnetic region, for integer spins only. This phase, which includes the isotropic point, has a finite energy gap and no long range order.Ground state properties of finite anisotropic antiferromagnetic Heisenberg chains are studied for odd half-integer spins S= 1 / 2 , 3 / 2 ... as well as integer spins S=1, 2 .... Finite size scaling analysis of the results clearly distinguishes the half-integer (S= 1 / 2 , 3 / 2 ) from the integer (S=1) spin situation. It gives strong support to a recent conjecture which postulates that the T=0 phase structure is very different in the two cases. According to this idea there exists a new phase between the planar and the antiferromagnetic region, for integer spins only. This phase, which includes the isotropic point, has a finite energy gap and no long range order.

Journal of Physics A Mathematical and GeneralDec 1, 198375 citations

Magnetic properties ofJ–J–J′ quantum Heisenberg chains with spinS= 1/2, 1, 3/2 and 2 in a magnetic field

Bo Gu, Gang Su, Song Gao

By means of the density matrix renormalization group (DMRG) method, the magnetic properties of the J-J-J $^{\prime}$ quantum Heisenberg chains with spin $S=1/2$ , 1, 3/2 and 2 in the ground states are investigated in the presence of a magnetic field. Two different cases are considered: (a) when $J$ is antiferromagnetic and $J^{\prime}$ is ferromagnetic (i.e. the AF-AF-F chain), the system is a ferrimagnet. The plateaus of the magnetization are observed. It is found that the width of the plateaus decreases with increasing the ferromagnetic coupling, and disappears when $% J^{\prime}/J$ passes over a critical value. The saturated field is observed to be independent of the ferromagnetic coupling; (b) when $J$ is ferromagnetic and $J^{\prime}$ is antiferromagnetic (i.e. the F-F-AF chain), the system becomes an antiferromagnet. The plateaus of the magnetization are also seen. The width of the plateaus decreases with decreasing the antiferromagnetic coupling, and disappears when $J^{\prime}/J $ passes over a critical value. Though the ground state properties are quite different, the magnetization plateaus in both cases tend to disappear when the ferromagnetic coupling becomes more dominant. Besides, no fundamental difference between the systems with spin half-integer and integer has been found.By means of the density matrix renormalization group (DMRG) method, the magnetic properties of the J-J-J$^{\prime}$ quantum Heisenberg chains with spin $S=1/2$, 1, 3/2 and 2 in the ground states are investigated in the presence of a magnetic field. Two different cases are considered: (a) when $J$ is antiferromagnetic and $J^{\prime}$ is ferromagnetic (i.e. the AF-AF-F chain), the system is a ferrimagnet. The plateaus of the magnetization are observed. It is found that the width of the plateaus decreases with increasing the ferromagnetic coupling, and disappears when $% J^{\prime}/J$ passes over a critical value. The saturated field is observed to be independent of the ferromagnetic coupling; (b) when $J$ is ferromagnetic and $J^{\prime}$ is antiferromagnetic (i.e. the F-F-AF chain), the system becomes an antiferromagnet. The plateaus of the magnetization are also seen. The width of the plateaus decreases with decreasing the antiferromagnetic coupling, and disappears when $J^{\prime}/J $ passes over a critical value. Though the ground state properties are quite different, the magnetization plateaus in both cases tend to disappear when the ferromagnetic coupling becomes more dominant. Besides, no fundamental difference between the systems with spin half-integer and integer has been found.

arXiv:cond-mat/0508685Journal of Physics Condensed MatterSep 9, 200527 citations

Edge states in open antiferromagnetic Heisenberg chains

Shaojin Qin, Tai Kai Ng, Zhao-Bin Su

We report our results in investigating edge effects of open antiferromagnetic Heisenberg spin chains with spin magnitudes S=1/2,1,3/2,2 using the density-matrix renormalization-group method initiated by White. For integer spin chains, we find that edge states with spin magnitude ${\mathit{S}}_{\mathrm{edge}}$ =S/2 exist, in agreement with the valence-bond-solid model picture. For half-integer spin chains, we find that no edge states exist for the S=1/2 spin chain, but an edge state exists in the S=3/2 spin chain with a ${\mathit{S}}_{\mathrm{edge}}$ =1/2, in agreement with a previous conjecture by Ng. The properties of the edge state in the S=3/2 chain is studied in detail. Strong finite-size effects associated with spin dimerization in half-integer spin chains are also discussed.We report our results in investigating edge effects of open antiferromagnetic Heisenberg spin chains with spin magnitudes S=1/2,1,3/2,2 using the density-matrix renormalization-group method initiated by White. For integer spin chains, we find that edge states with spin magnitude ${\mathit{S}}_{\mathrm{edge}}$=S/2 exist, in agreement with the valence-bond-solid model picture. For half-integer spin chains, we find that no edge states exist for the S=1/2 spin chain, but an edge state exists in the S=3/2 spin chain with a ${\mathit{S}}_{\mathrm{edge}}$=1/2, in agreement with a previous conjecture by Ng. The properties of the edge state in the S=3/2 chain is studied in detail. Strong finite-size effects associated with spin dimerization in half-integer spin chains are also discussed.

arXiv:cond-mat/9502047Physical review. B, Condensed matterNov 1, 199553 citations

We contrast, on the same figure, our phenomenological renormalization-group results on the

S=1

Heisenberg-Ising antiferromagnetic chain with results that we have recently obtained for

S=\frac{1}{2}

and

S=\frac{3}{2}

. The different behaviors of integer- and half-integer-spin chains are revealed very clearly. This confirms the conclusion of our Communication.

\frac{1}{2}

. Using finite-size scaling techniques, they conclude that between the

\mathrm{XY}

gapless phase and the doublet-ground-state N\'eel phase, a new phase appears in an extended anisotropy range. This phase, which encompasses the isotropic Heisenberg model, is characterized by a nonmagnetic singlet ground state and a nonzero excitation-energy gap. We perform a similar finite-chain scaling analysis on the spin-

\frac{1}{2}

antiferromagnetic Heisenberg-Ising chain and obtain strikingly similar results. Since the spin-

\frac{1}{4}

system is known rigorously not to exhibit the type of behavior proposed by Botet and Jullien, their analysis is open to doubt. The possibility arises that a strong singularity at the Heisenberg point for spin 1 (similar to the essential singularity for spin

\frac{1}{2}

) may be giving rise to misleading results. The

T=0

phase behavior of the spin-1 Heisenberg-Ising antiferromagnetic chain, therefore, remains in question and specific additional numerical studies are proposed to clarify the matter.

By means of the density matrix renormalization group (DMRG) method, the magnetic properties of the J-J-J

^{\prime}

quantum Heisenberg chains with spin

S=1/2

, 1, 3/2 and 2 in the ground states are investigated in the presence of a magnetic field. Two different cases are considered: (a) when

J

is antiferromagnetic and

J^{\prime}

is ferromagnetic (i.e. the AF-AF-F chain), the system is a ferrimagnet. The plateaus of the magnetization are observed. It is found that the width of the plateaus decreases with increasing the ferromagnetic coupling, and disappears when

% J^{\prime}/J

passes over a critical value. The saturated field is observed to be independent of the ferromagnetic coupling; (b) when

J

is ferromagnetic and

J^{\prime}

is antiferromagnetic (i.e. the F-F-AF chain), the system becomes an antiferromagnet. The plateaus of the magnetization are also seen. The width of the plateaus decreases with decreasing the antiferromagnetic coupling, and disappears when $J^{\prime}/J $ passes over a critical value. Though the ground state properties are quite different, the magnetization plateaus in both cases tend to disappear when the ferromagnetic coupling becomes more dominant. Besides, no fundamental difference between the systems with spin half-integer and integer has been found.

{\mathit{S}}_{\mathrm{edge}}

=S/2 exist, in agreement with the valence-bond-solid model picture. For half-integer spin chains, we find that no edge states exist for the S=1/2 spin chain, but an edge state exists in the S=3/2 spin chain with a

{\mathit{S}}_{\mathrm{edge}}

=1/2, in agreement with a previous conjecture by Ng. The properties of the edge state in the S=3/2 chain is studied in detail. Strong finite-size effects associated with spin dimerization in half-integer spin chains are also discussed.