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

Non-perturbative Quantum Effects

Magnetization plateaux in quasi 1d systems

Alessandro De Martino

Published Sep 25, 2000• 0 citations
Publisher

Abstract

We report results of theoretical investigations on the effect of doping and quenched disorder on the occurrence of plateaux in the magnetization curve of 1D systems with periodic modulations in the couplings.For single q-merized Hubbard chains, doping is shown to affect the position at which plateaux appear, leading to the emergence of plateaux at irrational values of the magnetization.For random bond antiferromagnetic Heisenberg chains with periodically modulated bond distributions, disorder generically removes the plateau structure, except in the case of discrete probability distributions.In the latter case, wide plateaux emerge at values of the magnetization dependent on the strength of disorder.

DOI
10.22323/1.006.0046

Related papers

Magnetization plateaux in periodically modulated 1D systems: eect of doping and disorder

Alessandro De Martino

We reportresultsoftheoreticalinvestigationsonthe eectofdopingandquencheddisor- derontheoccurrenceofplateauxinthemagnetizationcurveof1Dsystemswithperiodicmodulations inthe couplings. Forsingleq-merizedHubbardchains,dopingisshownto aectthe positionatwhich plateaux appear, leading to the emergence of plateaux atirrationalvalues of the magnetization. For random bond antiferromagnetic Heisenberg chains with periodically modulated bond distributions, disorder generically removes the plateau structure, except in the case of discrete probability distri- butions. In the latter case, wide plateaux emerge at values of the magnetization dependent on the strength of disorder.

•Jan 1, 2000•0 citations

Emergence of irrationality: Magnetization plateaus in modulated Hubbard chains

D. C. Cabra, Alessandro De Martino, A. Honecker +2 more

Hubbard chains with periodically modulated coupling constants in a magnetic field exhibit gaps at zero temperature in their magnetic and charge excitations in a variety of situations. In addition to fully gapped situations (plateau in the magnetization curve and charge gap), we have shown [Phys. Lett. A 268, 418 (2000)] that plateaus also appear in the presence of massless modes, leading to a plateau with a magnetization m whose value depends continuously on the filling n. Here we detail and extend the arguments leading to such doping-dependent magnetization plateaus. First we analyze the low-lying excitations using Abelian bosonization. We compute the susceptibility and show that due to the constraint of fixed n, it vanishes at low temperatures (thus leading to a magnetization plateau) even in the presence of one massless mode. Next we study correlation functions and show that one component of the superconducting order parameter develops quasi-long-range order on a doping-dependent magnetization plateau. We then use perturbation theory in the on-site repulsion U to compute the width of these plateaus up to first order in U. Finally, we compute ground state phase diagrams and correlation functions by Lanczos diagonalization of finite clusters, confirming the presence of doping-dependent plateaus and their special properties.

arXiv:cond-mat/0008333•Physical review. B, Condensed matter•Jan 30, 2001•20 citations

Random Bond XXZ Chains with Modulated Couplings

D. C. Cabra, Alessandro De Martino, Marcelo D. Grynberg +2 more

The magnetization behavior of q-periodic antiferromagnetic spin- 1/2 Heisenberg chains under uniform magnetic fields is investigated in a background of disorder exchange distributions. By means of both real space decimation procedures and numerical diagonalizations in XX chains, it is found that for binary disorder the magnetization exhibits wide plateaus at values of 1+2(p-1)/q, where p is the disorder strength. In contrast, no spin gaps are observed in the presence of continuous exchange distributions. We also study the magnetic susceptibility at low magnetic fields.

arXiv:cond-mat/0007205•Physical Review Letters•Nov 27, 2000•19 citations

Magnetization Plateaux in Random FrustratedS=1/2 Heisenberg Chains

Kazuo Hida

The $S=1/2$ frustrated Heisenberg chains with bond alternation is known to exhibit a magnetization plateau at half of the saturation magnetization $\Ms$ accompanied by the spontanuous translational symmetry breakdown. The effect of randomness on the magnetization process of this model is investigated. First we consider the mixture of the two kinds of chains both of which possess the $\Ms/2$-plateau in the common interval of the magnetization field. The plateau at $\Ms/2$ is found to vanish immediately if the randomness is switched on in agreement with Totsuka's prediction. The small plateau also appears near the saturation field due to the localization of inverted spins around the minority bond. On the other hand, if the stronger bond is replaced by the ferromagnetic bonds randomly, the randomness induced fractional plateau appears as in the nonfrustrated case. The plateau at $\Ms/2$ does not simply vanish but shifts and splits into two smaller plateaux. The magnetization on this plateau varies nonlinearly with $1-p$. The physical origin of this behavior is explained based on the strong coupling picture.

arXiv:cond-mat/0209074•Journal of the Physical Society of Japan•Apr 15, 2003•3 citations

Combined analytical and numerical approach to study magnetization plateaux in doped quasi-one-dimensional antiferromagnets

Carlos Alberto Lamas, Sylvain Capponi, Pierre Pujol

We investigate the magnetic properties of quasi-one-dimensional quantum spin-$S$ antiferromagnets. We use a combination of analytical and numerical techniques to study the presence of plateaux in the magnetization curve. The analytical technique consists in a path integral formulation in terms of coherent states. This technique can be extended to the presence of doping and has the advantage of a much better control for large spins than the usual bosonization technique. We discuss the appearance of doping-dependent plateaux in the magnetization curves for spin-$S$ chains and ladders. The analytical results are complemented by a density matrix renormalization group (DMRG) study for a trimerized spin-$1/2$ and anisotropic spin-$3/2$ doped chains.

arXiv:1105.3527•Physical Review B•Sep 21, 2011•15 citations

Coexistent quantum and classical aspects of magnetization plateaux in alternating-spin chains

Tôru Sakai, Shoji Yamamoto

The processes of magnetization of ferrimagnetic Heisenberg chains of alternating spins are studied theoretically. Size-scaling analysis with the exact diagonalization of finite systems for ( S , s ) = (3/2,1) and (2,1) indicates a multi-plateau structure in the ground-state magnetization curve for S and s >1/2. The first plateau in the spontaneous magnetization can be explained classically: as originating from the Ising gap. In contrast, the second and higher ones must be originating from the quantization of the magnetization. It is also found that all of the 2 s plateaux, both classical and quantum ones, appear even in the isotropic case with no bond alternation.

arXiv:cond-mat/0010446•Journal of Physics Condensed Matter•Nov 6, 2000•11 citations
We report results of theoretical investigations on the effect of doping and quenched disorder on the occurrence of plateaux in the magnetization curve of 1D systems with periodic modulations in the couplings.For single q-merized Hubbard chains, doping is shown to affect the position at which plateaux appear, leading to the emergence of plateaux at irrational values of the magnetization.For random bond antiferromagnetic Heisenberg chains with periodically modulated bond distributions, disorder generically removes the plateau structure, except in the case of discrete probability distributions.In the latter case, wide plateaux emerge at values of the magnetization dependent on the strength of disorder.
We reportresultsoftheoreticalinvestigationsonthe eectofdopingandquencheddisor- derontheoccurrenceofplateauxinthemagnetizationcurveof1Dsystemswithperiodicmodulations inthe couplings. Forsingleq-merizedHubbardchains,dopingisshownto aectthe positionatwhich plateaux appear, leading to the emergence of plateaux atirrationalvalues of the magnetization. For random bond antiferromagnetic Heisenberg chains with periodically modulated bond distributions, disorder generically removes the plateau structure, except in the case of discrete probability distri- butions. In the latter case, wide plateaux emerge at values of the magnetization dependent on the strength of disorder.
Hubbard chains with periodically modulated coupling constants in a magnetic field exhibit gaps at zero temperature in their magnetic and charge excitations in a variety of situations. In addition to fully gapped situations (plateau in the magnetization curve and charge gap), we have shown [Phys. Lett. A 268, 418 (2000)] that plateaus also appear in the presence of massless modes, leading to a plateau with a magnetization m whose value depends continuously on the filling n. Here we detail and extend the arguments leading to such doping-dependent magnetization plateaus. First we analyze the low-lying excitations using Abelian bosonization. We compute the susceptibility and show that due to the constraint of fixed n, it vanishes at low temperatures (thus leading to a magnetization plateau) even in the presence of one massless mode. Next we study correlation functions and show that one component of the superconducting order parameter develops quasi-long-range order on a doping-dependent magnetization plateau. We then use perturbation theory in the on-site repulsion U to compute the width of these plateaus up to first order in U. Finally, we compute ground state phase diagrams and correlation functions by Lanczos diagonalization of finite clusters, confirming the presence of doping-dependent plateaus and their special properties.
The magnetization behavior of q-periodic antiferromagnetic spin- 1/2 Heisenberg chains under uniform magnetic fields is investigated in a background of disorder exchange distributions. By means of both real space decimation procedures and numerical diagonalizations in XX chains, it is found that for binary disorder the magnetization exhibits wide plateaus at values of 1+2(p-1)/q, where p is the disorder strength. In contrast, no spin gaps are observed in the presence of continuous exchange distributions. We also study the magnetic susceptibility at low magnetic fields.
The S=1/2S=1/2S=1/2 frustrated Heisenberg chains with bond alternation is known to exhibit a magnetization plateau at half of the saturation magnetization $\Ms$ accompanied by the spontanuous translational symmetry breakdown. The effect of randomness on the magnetization process of this model is investigated. First we consider the mixture of the two kinds of chains both of which possess the $\Ms/2$-plateau in the common interval of the magnetization field. The plateau at $\Ms/2$ is found to vanish immediately if the randomness is switched on in agreement with Totsuka's prediction. The small plateau also appears near the saturation field due to the localization of inverted spins around the minority bond. On the other hand, if the stronger bond is replaced by the ferromagnetic bonds randomly, the randomness induced fractional plateau appears as in the nonfrustrated case. The plateau at $\Ms/2$ does not simply vanish but shifts and splits into two smaller plateaux. The magnetization on this plateau varies nonlinearly with 1−p1-p1−p. The physical origin of this behavior is explained based on the strong coupling picture.
We investigate the magnetic properties of quasi-one-dimensional quantum spin-SSS antiferromagnets. We use a combination of analytical and numerical techniques to study the presence of plateaux in the magnetization curve. The analytical technique consists in a path integral formulation in terms of coherent states. This technique can be extended to the presence of doping and has the advantage of a much better control for large spins than the usual bosonization technique. We discuss the appearance of doping-dependent plateaux in the magnetization curves for spin-SSS chains and ladders. The analytical results are complemented by a density matrix renormalization group (DMRG) study for a trimerized spin-1/21/21/2 and anisotropic spin-3/23/23/2 doped chains.
The processes of magnetization of ferrimagnetic Heisenberg chains of alternating spins are studied theoretically. Size-scaling analysis with the exact diagonalization of finite systems for ( S , s ) = (3/2,1) and (2,1) indicates a multi-plateau structure in the ground-state magnetization curve for S and s >1/2. The first plateau in the spontaneous magnetization can be explained classically: as originating from the Ising gap. In contrast, the second and higher ones must be originating from the quantization of the magnetization. It is also found that all of the 2 s plateaux, both classical and quantum ones, appear even in the isotropic case with no bond alternation.