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/9808312 · Physical review. B, Condensed matter

Strong-coupling approach to the magnetization process of polymerized quantum spin chains

A. Honecker

Published Mar 1, 1999• 29 citations
arXivHTMLPDF

Abstract

Polymerized quantum spin chains (i.e., spin chains with a periodic modulation of the coupling constants) exhibit plateaus in their magnetization curves when subjected to homogeneous external magnetic fields. We argue that the strong-coupling limit yields a simple but general explanation for the appearance of plateaus as well as of the associated quantization condition on the magnetization. We then proceed to explicitly compute series for the plateau boundaries of trimerized and quadrumerized spin-1/2 chains. The picture is completed by a discussion of how the universality classes associated with the transitions at the boundaries of magnetization plateaus arise in many cases from a first-order strong-coupling effective Hamiltonian.

DOI
10.1103/physrevb.59.6790

Related papers

Magnetization plateaux in N -leg spin ladders

D. C. Cabra, A. Honecker, Pierre Pujol

In this paper we continue and extend a systematic study of plateaux in magnetization curves of antiferromagnetic Heisenberg spin-1/2 ladders. We first review a bosonic field-theoretical formulation of a single $\mathrm{XXZ}$ chain in the presence of a magnetic field, which is then used for an Abelian bosonization analysis of $N$ weakly coupled chains. Predictions for the universality classes of the phase transitions at the plateaux boundaries are obtained in addition to a quantization condition for the value of the magnetization on a plateau. These results are complemented by and checked against strong-coupling expansions. Finally, we analyze the strong-coupling effective Hamiltonian for an odd number $N$ of cylindrically coupled chains numerically. For $N=3$ we explicitly observe a spin gap with a massive spinon-type fundamental excitation and obtain indications that this gap probably survives the limit $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$.

arXiv:cond-mat/9802035•Physical review. B, Condensed matter•Sep 1, 1998•227 citations

Ground-state magnetization of polymerized spin chains

D. C. Cabra, Marcelo D. Grynberg

We investigate the ground-state magnetization plateaus appearing in spin-1/2 polymerized Heisenberg chains under external magnetic fields. The associated fractional quantization scenario and the exponents which characterize the opening of gapful excitations are analyzed by means of Abelian bosonization methods. Our conclusions are fully supported by the extrapolated results obtained from Lanczos diagonalizations of finite systems.

arXiv:cond-mat/9803368•Physical review. B, Condensed matter•Jan 1, 1999•37 citations

Modified strong-coupling treatment of a spin-1/2 Heisenberg trimerized chain

Taras Verkholyak, Jozef Strečka

Quantum spin-1/2 antiferromagnetic Heisenberg trimerized chain with strong intradimer and weak monomer-dimer coupling constants is studied using the many-body perturbation expansion developed about the exact solution of the spin-1/2 Ising-Heisenberg diamond chain. The Heisenberg trimerized chain shows the intermediate one-third plateau, which was also observed in the magnetization curve of the polymeric compound Cu$_3$(P$_2$O$_6$OH)$_2$ affording its experimental realization. Within the strong-coupling method we have obtained the effective Hamiltonians for the magnetic-field range from zero to one-third plateau, and from one-third plateau to the saturation magnetization. The second-order perturbation theory shows reliable results even for the moderate ratio between weaker dimer-monomer and stronger intradimer coupling constants. We have also examined thermodynamic properties and recovered the low-temperature peak in the specific heat. The accuracy of the developed method is tested through a comparison with numerical density-matrix renormalization group and quantum Monte Carlo simulations. Using the results for the effective Hamiltonian we suggest straightforward procedure for finding the microscopic parameters of one-dimensional trimerized magnetic compounds with strong intradimer and weak monomer-dimer couplings. We found the refined values for the coupling constants of Cu$_3$(P$_2$O$_6$OH)$_2$ by matching the theoretical results with the available experimental data for the magnetization and magnetic susceptibility in a wide range of temperatures and magnetic fields.

•Jan 28, 2021•0 citations

Magnetization plateaus and phase diagram in polymerized S=1/2 XXZ chains

Wei Chen, Kazuo Hida, B. C. Sanctuary

The magnetization plateaus of polymerized $S=\frac{1}{2}$ $\mathrm{XXZ}$ chains are studied for general values of p. Two plateau-non-plateau critical lines and one plateau-plateau critical line are found for each value of p. The universality class of the plateau-non-plateau transition belongs to the Brezinskii-Kosterlitz-Thouless type and that of the plateau-plateau transition, to the Gaussian type. The critical points are determined by level spectroscopic analysis of the numerical diagonalization results for $4<~p<~8.$ The multicritical points are calculated using the integral equations based on the Bethe ansatz solution of the $\mathrm{XXZ}$ model. The behavior of multicritical points are analyzed in detail for large p. It is found that the plateau region is enhanced with the increase in periodicity p although the nonplateau region persists as far as p is finite.

arXiv:cond-mat/0009481•Physical review. B, Condensed matter•Mar 14, 2001•11 citations

Topological nature of magnetization plateaus in periodically modulated quantum spin chains

Haiping Hu, Chen Cheng, Zhihao Xu +2 more

We unveil nontrivial topological properties of zero-temperature magnetization plateau states in periodically modulated quantum spin chains under a uniform magnetic field. As positions of plateaus are uniquely determined by the modulation period of exchange couplings, we find that the topologically nontrivial plateau state can be characterized by a nonzero integer Chern number and has nontrivial edge excitations. Our study clarifies the topological origin of the well-known phenomena of quantized magnetization plateaus in one-dimensional quantum spin systems and relates the plateau state to the correlated topological insulator.

arXiv:1310.4551•Physical Review B•Jul 31, 2014•30 citations

Magnetization Plateaus in Antiferromagnetic-(Ferromagnetic)nPolymerizedS=1/2XXZ Chains

Wei Chen, Kazuo Hida, B. C. Sanctuary

The plateau-non-plateau transition in the antiferromagnetic-(ferromagnetic)$_{n}$ polymerized $S=1/2$ XXZ chains under the magnetic field is investigated. The universality class of this transition belongs to the Brezinskii-Kosterlitz-Thouless (BKT) type. The critical points are determined by level spectroscopy analysis of the numerical diagonalization data for $4 \leq p \leq 13$ where $p(\equiv n+1)$ is the size of a unit cell. It is found that the critical strength of ferromagnetic coupling decreases with $p$ for small $p$ but increases for larger enough $p$. It is also found that the plateau for large $p$ is wide enough for moderate values of exchange coupling so that it should be easily observed experimentally. This is in contrast to the plateaus for $p = 3$ chains which are narrow for a wide range of exchange coupling even away from the critical point.

arXiv:cond-mat/0005544•Journal of the Physical Society of Japan•Oct 15, 2000•5 citations
Polymerized quantum spin chains (i.e., spin chains with a periodic modulation of the coupling constants) exhibit plateaus in their magnetization curves when subjected to homogeneous external magnetic fields. We argue that the strong-coupling limit yields a simple but general explanation for the appearance of plateaus as well as of the associated quantization condition on the magnetization. We then proceed to explicitly compute series for the plateau boundaries of trimerized and quadrumerized spin-1/2 chains. The picture is completed by a discussion of how the universality classes associated with the transitions at the boundaries of magnetization plateaus arise in many cases from a first-order strong-coupling effective Hamiltonian.
In this paper we continue and extend a systematic study of plateaux in magnetization curves of antiferromagnetic Heisenberg spin-1/2 ladders. We first review a bosonic field-theoretical formulation of a single XXZ\mathrm{XXZ}XXZ chain in the presence of a magnetic field, which is then used for an Abelian bosonization analysis of NNN weakly coupled chains. Predictions for the universality classes of the phase transitions at the plateaux boundaries are obtained in addition to a quantization condition for the value of the magnetization on a plateau. These results are complemented by and checked against strong-coupling expansions. Finally, we analyze the strong-coupling effective Hamiltonian for an odd number NNN of cylindrically coupled chains numerically. For N=3N=3N=3 we explicitly observe a spin gap with a massive spinon-type fundamental excitation and obtain indications that this gap probably survives the limit $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$.
Quantum spin-1/2 antiferromagnetic Heisenberg trimerized chain with strong intradimer and weak monomer-dimer coupling constants is studied using the many-body perturbation expansion developed about the exact solution of the spin-1/2 Ising-Heisenberg diamond chain. The Heisenberg trimerized chain shows the intermediate one-third plateau, which was also observed in the magnetization curve of the polymeric compound Cu3_33​(P2_22​O6_66​OH)2_22​ affording its experimental realization. Within the strong-coupling method we have obtained the effective Hamiltonians for the magnetic-field range from zero to one-third plateau, and from one-third plateau to the saturation magnetization. The second-order perturbation theory shows reliable results even for the moderate ratio between weaker dimer-monomer and stronger intradimer coupling constants. We have also examined thermodynamic properties and recovered the low-temperature peak in the specific heat. The accuracy of the developed method is tested through a comparison with numerical density-matrix renormalization group and quantum Monte Carlo simulations. Using the results for the effective Hamiltonian we suggest straightforward procedure for finding the microscopic parameters of one-dimensional trimerized magnetic compounds with strong intradimer and weak monomer-dimer couplings. We found the refined values for the coupling constants of Cu3_33​(P2_22​O6_66​OH)2_22​ by matching the theoretical results with the available experimental data for the magnetization and magnetic susceptibility in a wide range of temperatures and magnetic fields.
The magnetization plateaus of polymerized S=12S=\frac{1}{2}S=21​ XXZ\mathrm{XXZ}XXZ chains are studied for general values of p. Two plateau-non-plateau critical lines and one plateau-plateau critical line are found for each value of p. The universality class of the plateau-non-plateau transition belongs to the Brezinskii-Kosterlitz-Thouless type and that of the plateau-plateau transition, to the Gaussian type. The critical points are determined by level spectroscopic analysis of the numerical diagonalization results for 4< p< 8.4<~p<~8.4< p< 8. The multicritical points are calculated using the integral equations based on the Bethe ansatz solution of the XXZ\mathrm{XXZ}XXZ model. The behavior of multicritical points are analyzed in detail for large p. It is found that the plateau region is enhanced with the increase in periodicity p although the nonplateau region persists as far as p is finite.
We unveil nontrivial topological properties of zero-temperature magnetization plateau states in periodically modulated quantum spin chains under a uniform magnetic field. As positions of plateaus are uniquely determined by the modulation period of exchange couplings, we find that the topologically nontrivial plateau state can be characterized by a nonzero integer Chern number and has nontrivial edge excitations. Our study clarifies the topological origin of the well-known phenomena of quantized magnetization plateaus in one-dimensional quantum spin systems and relates the plateau state to the correlated topological insulator.
The plateau-non-plateau transition in the antiferromagnetic-(ferromagnetic)n_{n}n​ polymerized S=1/2S=1/2S=1/2 XXZ chains under the magnetic field is investigated. The universality class of this transition belongs to the Brezinskii-Kosterlitz-Thouless (BKT) type. The critical points are determined by level spectroscopy analysis of the numerical diagonalization data for 4≤p≤134 \leq p \leq 134≤p≤13 where p(≡n+1)p(\equiv n+1)p(≡n+1) is the size of a unit cell. It is found that the critical strength of ferromagnetic coupling decreases with ppp for small ppp but increases for larger enough ppp. It is also found that the plateau for large ppp is wide enough for moderate values of exchange coupling so that it should be easily observed experimentally. This is in contrast to the plateaus for p=3p = 3p=3 chains which are narrow for a wide range of exchange coupling even away from the critical point.