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

arXiv:cond-mat/9709173 · Physical review. B, Condensed matter

Low-temperature properties of the spin-1 antiferromagnetic Heisenberg chain with bond alternation

Masanori Kohno, Minoru Takahashi, Masayuki Hagiwara

Published Jan 1, 1998• 34 citations
arXivHTMLPDF

Abstract

We investigate the low-temperature properties of the spin-1 antiferromagnetic Heisenberg chain with bond alternation by the quantum Monte Carlo method (loop algorithm). The strength of bond alternation at the gapless point is estimated as ${\ensuremath{\delta}}_{c}=0.2595\ifmmode\pm\else\textpm\fi{}0.0005.$ We confirm numerically that the low-temperature properties at the gapless point are consistent with field-theoretical predictions. The numerical results are compared with those of the spin-$1/2$ antiferromagnetic Heisenberg chain and recent experimental results for $[{{\mathrm{Ni}(333\ensuremath{-}\mathrm{t}\mathrm{e}\mathrm{t})(\mathrm{\ensuremath{\mu}}\ensuremath{-}\mathrm{N}}_{3}){}}_{n}]({\mathrm{ClO}}_{4}{)}_{n}$ [$333\ensuremath{-}\mathrm{t}\mathrm{e}\mathrm{t}=\mathrm{t}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{e}$ ${N,N}^{\ensuremath{'}}$-bis(3-aminopropyl)-1,3-propanediamine].

DOI
10.1103/physrevb.57.1046

Related papers

Low-temperature properties of quantum antiferromagnetic chains with alternating spins and

S. Brehmer, H.-J. Mikeska, Shoji Yamamoto

We study the low-temperature properties of S = 1 and S = 1/2 alternating spin chains with antiferromagnetic nearest-neighbour exchange couplings using analytical techniques as well as a quantum Monte Carlo method. The spin-wave approach predicts two different low-lying excitations, which are gapped and gapless, respectively. The structure of low-lying levels is also discussed using perturbation theory in terms of the strength of the Ising anisotropy. These analytical findings are compared with the results of quantum Monte Carlo calculations, and it turns out that spin-wave theory describes the present system well. We conclude that the quantum ferrimagnetic chain exhibits both ferromagnetic and antiferromagnetic aspects.

arXiv:cond-mat/9610109•Journal of Physics Condensed Matter•May 12, 1997•95 citations

Critical exponent η in S =1 antiferromagnetic Heisenberg chains with alternating interaction

Shoji Yamamoto

Low-temperature properties of S=1 antiferromagnetic Heisenberg chains with alternating interaction, scrH=${\mathit{Jtsum}}_{\mathit{i}}$[1-(-1${)}^{\mathit{i}}$\ensuremath{\delta}]${\mathrm{S}}_{\mathit{i}}$\ensuremath{\cdot}${\mathrm{S}}_{\mathit{i}+1}$, are studied by a quantum Monte Carlo method. Spatial distributions of the spin correlation function 〈${\mathit{S}}_{1}^{\mathit{z}}$${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$〉 and the local magnetic moment 〈${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$〉 are visualized as a function of \ensuremath{\delta}. The continuous phase transition at \ensuremath{\delta}=0.25, which was indicated by several authors, is confirmed by the \ensuremath{\delta} dependence of the low-lying level structure, the divergence of the correlation length, and also the collapse of the edge states. The critical exponent \ensuremath{\eta}, governing the power-law decay of the spin correlation function, is estimated to be 0.99\ifmmode\pm\else\textpm\fi{}0.05. The present result raises a possibility that the variety of quantum spin chains including not only the half-odd-integer-S ones but also the integer-S ones may be described in terms of the generic critical theory.

Physical review. B, Condensed matter•Oct 1, 1995•19 citations

Elementary excitations of S =1 antiferromagnetic Heisenberg chains with bond alternation

Shoji Yamamoto

A world-line quantum Monte Carlo method is employed to study the elementary excitations of S=1 antiferromagnetic Heisenberg chains with bond alternation described by the Hamiltonian, scrH=J ${\mathit{tsum}}_{\mathit{i}}$ [1-(-1${)}^{\mathit{i}}$\ensuremath{\delta}]${\mathrm{S}}_{\mathit{i}}$\ensuremath{\cdot}${\mathrm{S}}_{\mathit{i}+1}$. Imaginary-time correlation functions of this system at low-enough temperatures exhibit almost single-exponential decay and thus the lowest excitation spectrum can be successfully extracted from them. As \ensuremath{\delta} increases from 0 to 1, the system encounters a continuous phase transition at \ensuremath{\delta}\ensuremath{\simeq}0.25, where the energy(E)-momentum(q) relation is fitted well to the form E(q)=(${\mathit{v}}^{2}$ ${\mathrm{sin}}^{2}$q+${\mathrm{\ensuremath{\Delta}}}^{2}$${)}^{1/2}$ with the effective light velocity v=2.46\ifmmode\pm\else\textpm\fi{}0.08 and the energy gap \ensuremath{\Delta} which vanishes in the long chain limit. The central charge c at the massless critical point is estimated to be 1.02\ifmmode\pm\else\textpm\fi{}0.09, which suggests the universality class of the Gaussian model.

Physical review. B, Condensed matter•Jun 1, 1995•26 citations

Ground-State Properties ofS=1 Antiferromagnetic Heisenberg Chains with Bond Alternation

Shoji Yamamoto

Ground-state properties of S =1 antiferromagnetic Heisenberg chains with bond alternation, H = J ∑ i {1-(-1) i δ} S i · S i +1 , are studied by a quantum Monte Carlo method. Spin correlation between chain ends on the open chain appears for δ<0.25, while it vanishes for δ≥0.25. At δ≃0.25, the spin correlation length has a peak and the S =1/2 edge states for the open chain disappear. The fourfold degeneracy of the ground state of the open chain holds for δ<0.25, while it is removed for δ≥0.25. All the results support the continuous phase transition at δ≃0.25 demonstrated in the previous works.

Journal of the Physical Society of Japan•Dec 15, 1994•54 citations

S=3/2Antiferromagnetic Spin Chain with Bond Alternation

Makoto Yajima, Minoru Takahashi

The successive phase transitions of the Heisenberg spin chain with bond alternation, H = ∑ i =1 L -1 [1-(-1) i δ] S i · S i +1 , for the spin S =3/2 case under the open boundary condition are investigated by the density-matrix renormalization-group method proposed by White. Besides the Heisenberg point, we find that another gapless point exists at δ c = 0.42 ±0.02. This result qualitatively supports the field-theoretical prediction by Affleck and Haldane. However, our estimation of δ c deviates from the field-theoretical prediction, δ c = 2/3. We also find a fourfold degeneracy of the ground state in the region 0 <δ< δ c in the thermodynamic limit. Our results show that the degeneracy is described by the edge excitations, which is essentially similar to the one in the S =1 case. We calculate the string correlation function and find that its behavior is consistent with the valence-bond-solid (VBS) picture.

Journal of the Physical Society of Japan•Jan 15, 1996•23 citations

Low Energy Properties of the Random Spin-1/2 Ferromagnetic-Antiferromagnetic Heisenberg Chain

Kazuo Hida

The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet phase and the formation of the large-spin state is observed even for relatively small systems. For a small fraction of the ferromagnetic bond, the effect of the crossover to the random singlet phase on the low temperature susceptibility and specific heat is discussed. The crossover concentration of the ferromagnetic bond is estimated from the numerical data.

arXiv:cond-mat/9612232•Journal of the Physical Society of Japan•Feb 15, 1997•16 citations
We investigate the low-temperature properties of the spin-1 antiferromagnetic Heisenberg chain with bond alternation by the quantum Monte Carlo method (loop algorithm). The strength of bond alternation at the gapless point is estimated as \ensuremathδc=0.2595\ifmmode±\else\textpm\fi0.0005.{\ensuremath{\delta}}_{c}=0.2595\ifmmode\pm\else\textpm\fi{}0.0005.\ensuremathδc​=0.2595\ifmmode±\else\textpm\fi0.0005. We confirm numerically that the low-temperature properties at the gapless point are consistent with field-theoretical predictions. The numerical results are compared with those of the spin-1/21/21/2 antiferromagnetic Heisenberg chain and recent experimental results for [Ni(333\ensuremath−tet)(\ensuremathμ\ensuremath−N3)n](ClO4)n[{{\mathrm{Ni}(333\ensuremath{-}\mathrm{t}\mathrm{e}\mathrm{t})(\mathrm{\ensuremath{\mu}}\ensuremath{-}\mathrm{N}}_{3}){}}_{n}]({\mathrm{ClO}}_{4}{)}_{n}[Ni(333\ensuremath−tet)(\ensuremathμ\ensuremath−N3​)n​](ClO4​)n​ [333\ensuremath−tet=tetraamine333\ensuremath{-}\mathrm{t}\mathrm{e}\mathrm{t}=\mathrm{t}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{e}333\ensuremath−tet=tetraamine N,N\ensuremath′{N,N}^{\ensuremath{'}}N,N\ensuremath′-bis(3-aminopropyl)-1,3-propanediamine].
We study the low-temperature properties of S = 1 and S = 1/2 alternating spin chains with antiferromagnetic nearest-neighbour exchange couplings using analytical techniques as well as a quantum Monte Carlo method. The spin-wave approach predicts two different low-lying excitations, which are gapped and gapless, respectively. The structure of low-lying levels is also discussed using perturbation theory in terms of the strength of the Ising anisotropy. These analytical findings are compared with the results of quantum Monte Carlo calculations, and it turns out that spin-wave theory describes the present system well. We conclude that the quantum ferrimagnetic chain exhibits both ferromagnetic and antiferromagnetic aspects.
Low-temperature properties of S=1 antiferromagnetic Heisenberg chains with alternating interaction, scrH=Jtsumi{\mathit{Jtsum}}_{\mathit{i}}Jtsumi​[1-(-1)i{)}^{\mathit{i}})i\ensuremath{\delta}]Si{\mathrm{S}}_{\mathit{i}}Si​\ensuremath{\cdot}Si+1{\mathrm{S}}_{\mathit{i}+1}Si+1​, are studied by a quantum Monte Carlo method. Spatial distributions of the spin correlation function 〈S1z{\mathit{S}}_{1}^{\mathit{z}}S1z​Siz{\mathit{S}}_{\mathit{i}}^{\mathit{z}}Siz​〉 and the local magnetic moment 〈Siz{\mathit{S}}_{\mathit{i}}^{\mathit{z}}Siz​〉 are visualized as a function of \ensuremath{\delta}. The continuous phase transition at \ensuremath{\delta}=0.25, which was indicated by several authors, is confirmed by the \ensuremath{\delta} dependence of the low-lying level structure, the divergence of the correlation length, and also the collapse of the edge states. The critical exponent \ensuremath{\eta}, governing the power-law decay of the spin correlation function, is estimated to be 0.99\ifmmode\pm\else\textpm\fi{}0.05. The present result raises a possibility that the variety of quantum spin chains including not only the half-odd-integer-S ones but also the integer-S ones may be described in terms of the generic critical theory.
A world-line quantum Monte Carlo method is employed to study the elementary excitations of S=1 antiferromagnetic Heisenberg chains with bond alternation described by the Hamiltonian, scrH=J tsumi{\mathit{tsum}}_{\mathit{i}}tsumi​ [1-(-1)i{)}^{\mathit{i}})i\ensuremath{\delta}]Si{\mathrm{S}}_{\mathit{i}}Si​\ensuremath{\cdot}Si+1{\mathrm{S}}_{\mathit{i}+1}Si+1​. Imaginary-time correlation functions of this system at low-enough temperatures exhibit almost single-exponential decay and thus the lowest excitation spectrum can be successfully extracted from them. As \ensuremath{\delta} increases from 0 to 1, the system encounters a continuous phase transition at \ensuremath{\delta}\ensuremath{\simeq}0.25, where the energy(E)-momentum(q) relation is fitted well to the form E(q)=(v2{\mathit{v}}^{2}v2 sin2{\mathrm{sin}}^{2}sin2q+${\mathrm{\ensuremath{\Delta}}}^{2}$)1/2{)}^{1/2})1/2 with the effective light velocity v=2.46\ifmmode\pm\else\textpm\fi{}0.08 and the energy gap \ensuremath{\Delta} which vanishes in the long chain limit. The central charge c at the massless critical point is estimated to be 1.02\ifmmode\pm\else\textpm\fi{}0.09, which suggests the universality class of the Gaussian model.
Ground-state properties of S =1 antiferromagnetic Heisenberg chains with bond alternation, H = J ∑ i {1-(-1) i δ} S i · S i +1 , are studied by a quantum Monte Carlo method. Spin correlation between chain ends on the open chain appears for δ<0.25, while it vanishes for δ≥0.25. At δ≃0.25, the spin correlation length has a peak and the S =1/2 edge states for the open chain disappear. The fourfold degeneracy of the ground state of the open chain holds for δ<0.25, while it is removed for δ≥0.25. All the results support the continuous phase transition at δ≃0.25 demonstrated in the previous works.
The successive phase transitions of the Heisenberg spin chain with bond alternation, H = ∑ i =1 L -1 [1-(-1) i δ] S i · S i +1 , for the spin S =3/2 case under the open boundary condition are investigated by the density-matrix renormalization-group method proposed by White. Besides the Heisenberg point, we find that another gapless point exists at δ c = 0.42 ±0.02. This result qualitatively supports the field-theoretical prediction by Affleck and Haldane. However, our estimation of δ c deviates from the field-theoretical prediction, δ c = 2/3. We also find a fourfold degeneracy of the ground state in the region 0 <δ< δ c in the thermodynamic limit. Our results show that the degeneracy is described by the edge excitations, which is essentially similar to the one in the S =1 case. We calculate the string correlation function and find that its behavior is consistent with the valence-bond-solid (VBS) picture.
The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet phase and the formation of the large-spin state is observed even for relatively small systems. For a small fraction of the ferromagnetic bond, the effect of the crossover to the random singlet phase on the low temperature susceptibility and specific heat is discussed. The crossover concentration of the ferromagnetic bond is estimated from the numerical data.