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 the Physical Society of Japan

AnisotropicS=1 Antiferromagnetic Heisenberg Chain in a Magnetic Field

Tôru Sakai, Minoru Takahashi

Published Feb 15, 1993• 13 citations
Publisher

Abstract

We study the S =1 antiferromagnetic Heisenberg chain with the anisotropies E ∑ j [( S j x ) 2 -( S j y ) 2 ] and D ∑ j ( S j x ) 2 in a magnetic field H along z -axis, using numerical diagonalization up to N =14 and the finite-size scaling and phenomenological renormalization. We give the phase diagrams in the H E and H D planes repectively at T =0. It is found that a magnetic field breaking the axial symmetry of the Hamiltonian brings about canted Néel order for H c1 < H < H c2 , if the system has the Haldane gap. The two transitions at H c1 and H c2 are revealed to belong to the same universality class as the two-dimensional Ising model. In addition it is found that even if the system is in the large- D phase ( D > D c ≈1), the same transitions occur in the region where the value of D is about 1.0∼1.5.

DOI
10.1143/jpsj.62.750

Related papers

S=1 antiferromagnetic Heisenberg chain with an axial-symmetry-breaking anisotropy

Tiôru Sakai, Minoru Takahashi

The ground state of the S=1 antiferromagnetic Heisenberg chain with an axial-symmetry-breaking anisotropy ${\mathit{E}\mathit{tsum}}_{\mathit{j}}$ [(${\mathit{S}}_{\mathit{j}}^{\mathit{x}}$${)}^{2}$-(${\mathit{S}}_{\mathit{j}}^{\mathit{y}}$${)}^{2}$] is studied by the finite-size scaling and phenomenological renormalization-group technique based on numerical diagonalizations up to N=14. It is found that two phase transitions exist at ${\mathit{E}}_{\mathit{c}1}$=0.20\ifmmode\pm\else\textpm\fi{}0.01 and ${\mathit{E}}_{\mathit{c}2}$=1.71\ifmmode\pm\else\textpm\fi{}0.01, and both transitions belong to the same universality class as the two-dimensional Ising model.

Physical review. B, Condensed matter•Nov 1, 1991•5 citations

Transverse Antiferromagnetism of a Magnetized Haldane-Gap System

Tôru Sakai, Minoru Takahashi

A 1D S =1 Heisenberg antiferromagnet in a magnetic field H (// z -axis) at T =0 is studied by numerical diagonalizations. It is found that a phase transition exists at H c1 (=Δ), where Δ is the Haldane gap, and the transverse staggered susceptibility χ st x x diverges and the spin correlation is asymptotically < S 0 x S r x >∼(-1) r r -η between H c1 and H c2 (=4). If the system is quasi-1D, even small interchain interactions can make canting Néel order within a mean field approximation for interchain interactions. This is consistent with a recent NMR measurement for NENP at low temperature.

Journal of the Physical Society of Japan•Dec 15, 1990•1 citation

S=1 antiferromagnetic Heisenberg chain in a magnetic field

Tôru Sakai, Minoru Takahashi

A one-dimensional S=1 Heisenberg antiferromagnet in a magnetic field H (\ensuremath{\parallel}z axis) at T=0 is studied by numerical diagonalizations up to N=16. We give the magnetization curve at the thermodynamic limit, and derive an anomaly at ${\mathit{H}}_{\mathit{c}1}$ (=\ensuremath{\Delta}), where \ensuremath{\Delta} is the Haldane gap. It is also found that the transverse spin correlation has the asymptotic form 〈${\mathit{S}}_{0}^{\mathit{x}}$${\mathit{S}}_{\mathit{r}}^{\mathit{x}}$〉\ensuremath{\sim}(-1${)}^{\mathit{r}}$${\mathit{r}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\eta}}}$, and the transverse staggered susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{st}}^{\mathit{x}\mathit{x}}$ diverges between ${\mathit{H}}_{\mathit{c}1}$ and ${\mathit{H}}_{\mathit{c}2}$ (=4). The exponent \ensuremath{\eta} has a minimum (\ensuremath{\eta}\ensuremath{\simeq}0.3) at magnetization m\ensuremath{\simeq}1/3 and \ensuremath{\eta}\ensuremath{\simeq}0.5 at ${\mathit{H}}_{\mathit{c}1}$ and ${\mathit{H}}_{\mathit{c}2}$. If the system is quasi-one-dimensional, even small interchain couplings can create a canted N\'eel order, within a mean-field approximation for interchain interactions. This is consistent with a recent NMR measurement for Ni(${\mathrm{C}}_{2}$${\mathrm{H}}_{8}$${\mathrm{N}}_{2}$${)}_{2}$${\mathrm{NO}}_{2}$(${\mathrm{ClO}}_{4}$) (NENP) at low temperature.

Physical review. B, Condensed matter•Jun 1, 1991•150 citations

Ground-State Phase Diagram and Magnetization Curves of the Spin-1 Antiferromagnetic Heisenberg Chain with Bond Alternation and Uniaxial Single-Ion-Type Anisotropy

Takashi Tonegawa, Takeshi Nakao, Makoto Kaburagi

Ground-state properties of the spin-1 antiferromagnetic Heisenberg chain with bond alternation and uniaxial single-ion-type anisotropy, which is described by the Hamiltonian \({\cal H}_0 = \sum_{\ell=1}^N\{1-(-1)^\ell\alpha\}{\mib S}_\ell\cdot{\mib S}_{\ell+1} + D\sum_{\ell=1}^N\;(S_\ell^z)^2\) (0.0 ≤α≤1.0, -∞< D < ∞), are studied. An exact diagonalization method by means of the Lanczös technique is used. The ground-state phase diagram on the α versus D plane at the thermodynamic limit is determined by analyzing the Binder parameters associated with Néel order and z -direction string order for finite-size ( N = 6, 8, …, 16) chains. It is found that there exists a multicritical point at which the Haldane, Néel, and singlet-dimer phases meet and that the singlet-dimer phase and the large- D phase belong to the same unique phase. The ground-state magnetization curves at the thermodynamic limit for various values of α and D are obtained for the system described by the Hamiltonian, H 0 plus the Zeeman term - H ∑ ℓ=1 N S ℓ z . The results show that the 1/2-plateau appears in the magnetization curve at least when D ≥0.0 and \(0.0\lesssim\alpha \leq 1.0\).

Journal of the Physical Society of Japan•Oct 15, 1996•138 citations

Antiferromagnetic Ising chain in a mixed transverse and longitudinal magnetic field

А. А. Овчинников, Д. В. Дмитриев, V. Ya. Krivnov +1 more

We have studied the antiferromagnetic Ising chain in a transverse magnetic field ${h}_{x}$ and uniform longitudinal field ${h}_{z}.$ Using the density-matrix renormalization group calculation combined with a finite-size scaling the ground-state phase diagram in ${(h}_{x}{,h}_{z})$ plane is determined. It is shown that there is an order-disordered transition line in this plane and the critical properties belong to the universality class of the two-dimensional Ising model. Based on the perturbation theory in ${h}_{z}$ the scaling behavior of the mass gap in the vicinity of the critical point ${(h}_{x}{=1/2,h}_{z}=0)$ is established. It is found that the form of the transition line near the classical multicritical point ${(h}_{x}{=0,h}_{z}=1)$ is linear. The connection of the considered quantum model with the quasi-one-dimensional classical Ising model in the magnetic field is discussed.

arXiv:cond-mat/0306468•Physical review. B, Condensed matter•Dec 5, 2003•125 citations

Effect of a Symmetry-Breaking Field on the Ground State of the Spin-1/2 Antiferromagnetic Linear Chain

Shigeyoshi Mori, Jong-Jae Kim, Isao Harada

We investigate the ground-state property of the one-dimensional spin-1/2 antiferromagnetic X X Z chain in a symmetry-breaking field, by means of numerical diagonalization method for finite-size spin systems combined with the phenomenological renormalization group method. It is found that, with increasing field, there occurs the ground-state phase transition from an ordered phase to a disordered phase, whose critical property belongs to the universality class of the transverse Ising model. The ground-state phase diagram is determined in two parameter regions; (i) an Ising-like region and (ii) an X Y -like region. Our inspection of the field dependence of the energy gap and the static spin structure factors reveals that the ordered phase in both regions exhibits the characteristics of Néel order. Quantum nature of the ground state is also briefly discussed.

Journal of the Physical Society of Japan•Sep 15, 1995•19 citations
We study the S =1 antiferromagnetic Heisenberg chain with the anisotropies E ∑ j [( S j x ) 2 -( S j y ) 2 ] and D ∑ j ( S j x ) 2 in a magnetic field H along z -axis, using numerical diagonalization up to N =14 and the finite-size scaling and phenomenological renormalization. We give the phase diagrams in the H E and H D planes repectively at T =0. It is found that a magnetic field breaking the axial symmetry of the Hamiltonian brings about canted Néel order for H c1 < H < H c2 , if the system has the Haldane gap. The two transitions at H c1 and H c2 are revealed to belong to the same universality class as the two-dimensional Ising model. In addition it is found that even if the system is in the large- D phase ( D > D c ≈1), the same transitions occur in the region where the value of D is about 1.0∼1.5.
The ground state of the S=1 antiferromagnetic Heisenberg chain with an axial-symmetry-breaking anisotropy Etsumj{\mathit{E}\mathit{tsum}}_{\mathit{j}}Etsumj​ [(Sjx{\mathit{S}}_{\mathit{j}}^{\mathit{x}}Sjx​)2{)}^{2})2-(Sjy{\mathit{S}}_{\mathit{j}}^{\mathit{y}}Sjy​)2{)}^{2})2] is studied by the finite-size scaling and phenomenological renormalization-group technique based on numerical diagonalizations up to N=14. It is found that two phase transitions exist at Ec1{\mathit{E}}_{\mathit{c}1}Ec1​=0.20\ifmmode\pm\else\textpm\fi{}0.01 and Ec2{\mathit{E}}_{\mathit{c}2}Ec2​=1.71\ifmmode\pm\else\textpm\fi{}0.01, and both transitions belong to the same universality class as the two-dimensional Ising model.
A 1D S =1 Heisenberg antiferromagnet in a magnetic field H (// z -axis) at T =0 is studied by numerical diagonalizations. It is found that a phase transition exists at H c1 (=Δ), where Δ is the Haldane gap, and the transverse staggered susceptibility χ st x x diverges and the spin correlation is asymptotically < S 0 x S r x >∼(-1) r r -η between H c1 and H c2 (=4). If the system is quasi-1D, even small interchain interactions can make canting Néel order within a mean field approximation for interchain interactions. This is consistent with a recent NMR measurement for NENP at low temperature.
A one-dimensional S=1 Heisenberg antiferromagnet in a magnetic field H (\ensuremath{\parallel}z axis) at T=0 is studied by numerical diagonalizations up to N=16. We give the magnetization curve at the thermodynamic limit, and derive an anomaly at Hc1{\mathit{H}}_{\mathit{c}1}Hc1​ (=\ensuremath{\Delta}), where \ensuremath{\Delta} is the Haldane gap. It is also found that the transverse spin correlation has the asymptotic form 〈S0x{\mathit{S}}_{0}^{\mathit{x}}S0x​Srx{\mathit{S}}_{\mathit{r}}^{\mathit{x}}Srx​〉\ensuremath{\sim}(-1)r{)}^{\mathit{r}})r${\mathit{r}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\eta}}}$, and the transverse staggered susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{st}}^{\mathit{x}\mathit{x}}$ diverges between Hc1{\mathit{H}}_{\mathit{c}1}Hc1​ and Hc2{\mathit{H}}_{\mathit{c}2}Hc2​ (=4). The exponent \ensuremath{\eta} has a minimum (\ensuremath{\eta}\ensuremath{\simeq}0.3) at magnetization m\ensuremath{\simeq}1/3 and \ensuremath{\eta}\ensuremath{\simeq}0.5 at Hc1{\mathit{H}}_{\mathit{c}1}Hc1​ and Hc2{\mathit{H}}_{\mathit{c}2}Hc2​. If the system is quasi-one-dimensional, even small interchain couplings can create a canted N\'eel order, within a mean-field approximation for interchain interactions. This is consistent with a recent NMR measurement for Ni(C2{\mathrm{C}}_{2}C2​H8{\mathrm{H}}_{8}H8​N2{\mathrm{N}}_{2}N2​)2{)}_{2})2​NO2{\mathrm{NO}}_{2}NO2​(ClO4{\mathrm{ClO}}_{4}ClO4​) (NENP) at low temperature.
Ground-state properties of the spin-1 antiferromagnetic Heisenberg chain with bond alternation and uniaxial single-ion-type anisotropy, which is described by the Hamiltonian \({\cal H}_0 = \sum_{\ell=1}^N\{1-(-1)^\ell\alpha\}{\mib S}_\ell\cdot{\mib S}_{\ell+1} + D\sum_{\ell=1}^N\;(S_\ell^z)^2\) (0.0 ≤α≤1.0, -∞< D < ∞), are studied. An exact diagonalization method by means of the Lanczös technique is used. The ground-state phase diagram on the α versus D plane at the thermodynamic limit is determined by analyzing the Binder parameters associated with Néel order and z -direction string order for finite-size ( N = 6, 8, …, 16) chains. It is found that there exists a multicritical point at which the Haldane, Néel, and singlet-dimer phases meet and that the singlet-dimer phase and the large- D phase belong to the same unique phase. The ground-state magnetization curves at the thermodynamic limit for various values of α and D are obtained for the system described by the Hamiltonian, H 0 plus the Zeeman term - H ∑ ℓ=1 N S ℓ z . The results show that the 1/2-plateau appears in the magnetization curve at least when D ≥0.0 and 0.0≲α≤1.00.0\lesssim\alpha \leq 1.00.0≲α≤1.0.
We have studied the antiferromagnetic Ising chain in a transverse magnetic field hx{h}_{x}hx​ and uniform longitudinal field hz.{h}_{z}.hz​. Using the density-matrix renormalization group calculation combined with a finite-size scaling the ground-state phase diagram in (hx,hz){(h}_{x}{,h}_{z})(hx​,hz​) plane is determined. It is shown that there is an order-disordered transition line in this plane and the critical properties belong to the universality class of the two-dimensional Ising model. Based on the perturbation theory in hz{h}_{z}hz​ the scaling behavior of the mass gap in the vicinity of the critical point (hx=1/2,hz=0){(h}_{x}{=1/2,h}_{z}=0)(hx​=1/2,hz​=0) is established. It is found that the form of the transition line near the classical multicritical point (hx=0,hz=1){(h}_{x}{=0,h}_{z}=1)(hx​=0,hz​=1) is linear. The connection of the considered quantum model with the quasi-one-dimensional classical Ising model in the magnetic field is discussed.
We investigate the ground-state property of the one-dimensional spin-1/2 antiferromagnetic X X Z chain in a symmetry-breaking field, by means of numerical diagonalization method for finite-size spin systems combined with the phenomenological renormalization group method. It is found that, with increasing field, there occurs the ground-state phase transition from an ordered phase to a disordered phase, whose critical property belongs to the universality class of the transverse Ising model. The ground-state phase diagram is determined in two parameter regions; (i) an Ising-like region and (ii) an X Y -like region. Our inspection of the field dependence of the energy gap and the static spin structure factors reveals that the ordered phase in both regions exhibits the characteristics of Néel order. Quantum nature of the ground state is also briefly discussed.