arXiv:cond-mat/0608326 · Physical Review B

Excitations with fractional spin less than 12 in frustrated magnetoelastic chains

C. J. Gazza, A. Dobry, D. C. Cabra, T. Vekua

Published Apr 10, 2007• 11 citations

Abstract

We study the magnetic excitations on top of the plateaux states recently discovered in spin-Peierls systems in a magnetic field. We show by means of extensive density matrix renormalization group (DMRG) computations and an analytic approach that one single spin-flip on top of $M=1\ensuremath{-}\frac{2}{N}$ $(N=3,4,\dots{})$ plateau decays into $N$ elementary excitations each carrying a fraction $\frac{1}{N}$ of the spin. This fractionalization goes beyond the well-known decay of one magnon into two spinons taking place on top of the $M=0$ plateau. Concentrating on the $\frac{1}{3}$ plateau $(N=3)$ we unravel the microscopic structure of the domain walls which carry fractional spin-$\frac{1}{3}$, both from theory and numerics. These excitations are shown to be noninteracting and should be observable in x-ray and nuclear magnetic resonance experiments.

DOI: 10.1103/physrevb.75.165104

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Fractional Sz excitation and its bound state around the 1/3 plateau of the S=1/2 Ising-like zigzag XXZ chain

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arXiv:cond-mat/0608326 · Physical Review B

Excitations with fractional spin less than 12 in frustrated magnetoelastic chains

C. J. Gazza, A. Dobry, D. C. Cabra, T. Vekua

Published Apr 10, 2007• 11 citations

arXiv HTML PDF

Abstract

M=1\ensuremath{-}\frac{2}{N}

(N=3,4,\dots{})

plateau decays into

N

elementary excitations each carrying a fraction

\frac{1}{N}

of the spin. This fractionalization goes beyond the well-known decay of one magnon into two spinons taking place on top of the

M=0

plateau. Concentrating on the

\frac{1}{3}

plateau

(N=3)

we unravel the microscopic structure of the domain walls which carry fractional spin-

\frac{1}{3}

, both from theory and numerics. These excitations are shown to be noninteracting and should be observable in x-ray and nuclear magnetic resonance experiments.

DOI: 10.1103/physrevb.75.165104

Related papers

FractionalSzExcitation and Its Boundstate for theS=1/2 Antiferromagnetic Zigzag Spin Chain in a Magnetic Field

Kouichi Okunishi, Takashi Tonegawa

We demonstrate that domain-wall type excitations carrying the fractional magnetization $S^z=\pm1/3$ and their bound state describe the low-energy physics around the 1/3 plateau of the antiferromagnetic zigzag spin chain in the strongly frustrated region. In particular we discuss the relevance of such domain-wall excitations to the characteristic properties of the magnetization curves: the 1/3 plateau accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve.We demonstrate that domain-wall type excitations carrying the fractional magnetization $S^z=\pm1/3$ and their bound state describe the low-energy physics around the 1/3 plateau of the antiferromagnetic zigzag spin chain in the strongly frustrated region. In particular we discuss the relevance of such domain-wall excitations to the characteristic properties of the magnetization curves: the 1/3 plateau accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve.

arXiv:cond-mat/0505719Journal of the Physical Society of JapanJan 1, 20054 citations

Condensation of magnons and spinons in a frustrated ladder

J.-B. Fouet, Frédéric Mila, D. Clarke +4 more

Motivated by the ever-increasing experimental effort devoted to the properties of frustrated quantum magnets in a magnetic field, we present a careful and detailed theoretical analysis of a one-dimensional version of this problem, a frustrated ladder with a magnetization plateau at $m=1∕2$ . We show that even for purely isotropic Heisenberg interactions, the magnetization curve exhibits a rather complex behavior that can be fully accounted for in terms of simple elementary excitations. The introduction of anisotropic interactions (e.g., Dzyaloshinskii-Moriya interactions) modifies significantly the picture and reveals an essential difference between integer and fractional plateaus. In particular, anisotropic interactions generically open a gap in the region between the plateaus, but we show that this gap closes upon entering fractional plateaus. All of these conclusions, based on analytical arguments, are supported by extensive density matrix renormalization group calculations.Motivated by the ever-increasing experimental effort devoted to the properties of frustrated quantum magnets in a magnetic field, we present a careful and detailed theoretical analysis of a one-dimensional version of this problem, a frustrated ladder with a magnetization plateau at $m=1∕2$. We show that even for purely isotropic Heisenberg interactions, the magnetization curve exhibits a rather complex behavior that can be fully accounted for in terms of simple elementary excitations. The introduction of anisotropic interactions (e.g., Dzyaloshinskii-Moriya interactions) modifies significantly the picture and reveals an essential difference between integer and fractional plateaus. In particular, anisotropic interactions generically open a gap in the region between the plateaus, but we show that this gap closes upon entering fractional plateaus. All of these conclusions, based on analytical arguments, are supported by extensive density matrix renormalization group calculations.

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Magnetization plateaus emerging in quantum spin systems due to spontaneously breaking of translational symmetry have been reported both theoretically and experimentally. The broken symmetry can induce reconstruction of elementary excitations such as Goldstone and Higgs modes, whereas its microscopic mechanism and reconstructed quasiparticle in magnetization-plateau phases have remained unclear so far. Here we theoretically study magnetic excitations in the magnetization-plateau phases of a frustrated spin ladder by using the dynamical density-matrix renormalization-group method. Additionally, analytical approaches with the perturbation theory are performed to obtain an intuitive view of magnetic excitations. A comparison between numerical and analytical results indicates the presence of a reconstructed quasiparticle originating from spontaneously broken translational symmetry, which is realized as a collective mode of the spin trimer called a trimeron.Magnetization plateaus emerging in quantum spin systems due to spontaneously breaking of translational symmetry have been reported both theoretically and experimentally. The broken symmetry can induce reconstruction of elementary excitations such as Goldstone and Higgs modes, whereas its microscopic mechanism and reconstructed quasiparticle in magnetization-plateau phases have remained unclear so far. Here we theoretically study magnetic excitations in the magnetization-plateau phases of a frustrated spin ladder by using the dynamical density-matrix renormalization-group method. Additionally, analytical approaches with the perturbation theory are performed to obtain an intuitive view of magnetic excitations. A comparison between numerical and analytical results indicates the presence of a reconstructed quasiparticle originating from spontaneously broken translational symmetry, which is realized as a collective mode of the spin trimer called a trimeron.

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We study the dynamical structure factor of the frustrated spin-$3/2\phantom{\rule{4pt}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg chains, with particular focus on the partially dimerized phase that emerges between two Kosterlitz-Thouless transitions. Using a valence bond solid Ansatz corroborated by density-matrix renormalization-group simulations, we investigate the nature of magnon and spinon excitations through the single-mode approximation. We show that the magnon develops an incommensurate dispersion at ${J}_{2}\ensuremath{\approx}0.32{J}_{1}$, while the spinons, viewed as domain walls between degenerate valence bond solid states, become incommensurate at ${J}_{2}\ensuremath{\approx}0.4{J}_{1}$ beyond the Lifshitz point $({J}_{2}\ensuremath{\approx}0.388{J}_{1})$. The dynamical structure factor exhibits rich spectral features shaped by the interplay between these excitations, with magnons appearing as resonances embedded in the spinon continuum. The spinon gap shows a nonmonotonic behavior, reaching a peak near the center of the partially dimerized phase and closing at the boundaries, suggesting the appearance of a floating phase as a result of the condensation of incommensurate spinons. Comparative analysis with the spin- $5/2$ case confirms the universality of these phenomena across half-integer higher-spin systems. Our results provide detailed insight into how fractionalization and incommensurate condensation govern the spectral properties of frustrated spin chains, offering a unified picture across different spin magnitudes.We study the dynamical structure factor of the frustrated spin-$3/2\phantom{\rule{4pt}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg chains, with particular focus on the partially dimerized phase that emerges between two Kosterlitz-Thouless transitions. Using a valence bond solid Ansatz corroborated by density-matrix renormalization-group simulations, we investigate the nature of magnon and spinon excitations through the single-mode approximation. We show that the magnon develops an incommensurate dispersion at ${J}_{2}\ensuremath{\approx}0.32{J}_{1}$, while the spinons, viewed as domain walls between degenerate valence bond solid states, become incommensurate at ${J}_{2}\ensuremath{\approx}0.4{J}_{1}$ beyond the Lifshitz point $({J}_{2}\ensuremath{\approx}0.388{J}_{1})$. The dynamical structure factor exhibits rich spectral features shaped by the interplay between these excitations, with magnons appearing as resonances embedded in the spinon continuum. The spinon gap shows a nonmonotonic behavior, reaching a peak near the center of the partially dimerized phase and closing at the boundaries, suggesting the appearance of a floating phase as a result of the condensation of incommensurate spinons. Comparative analysis with the spin-$5/2$ case confirms the universality of these phenomena across half-integer higher-spin systems. Our results provide detailed insight into how fractionalization and incommensurate condensation govern the spectral properties of frustrated spin chains, offering a unified picture across different spin magnitudes.

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Frustration-induced plateaus in S≥12 Heisenberg spin ladders

Frédéric Michaud, Tommaso Coletta, Salvatore R. Manmana +2 more

We study the $T=0$ magnetization of frustrated two-leg spin ladders with arbitrary value of the spin $S$ . In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins $S$ and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaus. These ratios depend both on the plateau and on the spin. To confirm these results and to investigate the properties of these ladders away from the strong-coupling limit, we have performed extensive density-matrix renormalization-group calculations for $S\ensuremath{\le}2$. For large enough inter-rung couplings, all plateaus simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.We study the $T=0$ magnetization of frustrated two-leg spin ladders with arbitrary value of the spin $S$. In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins $S$ and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaus. These ratios depend both on the plateau and on the spin. To confirm these results and to investigate the properties of these ladders away from the strong-coupling limit, we have performed extensive density-matrix renormalization-group calculations for $S\ensuremath{\le}2$. For large enough inter-rung couplings, all plateaus simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.

arXiv:0907.1461Physical Review BJan 8, 201027 citations

Fractional Sz excitation and its bound state around the 1/3 plateau of the S=1/2 Ising-like zigzag XXZ chain

Kouichi Okunishi, Takashi Tonegawa

We present the microscopic view for the excitations around the 1/3 plateau state of the Ising-like zigzag $\mathrm{XXZ}$ chain. We analyze the low-energy excitations around the plateau with the degenerating perturbation theory from the Ising limit, combined with the Bethe-form wave function. We then find that the domain-wall particles carrying ${S}^{z}=\ifmmode\pm\else\textpm\fi{}1/3$ and its bound state of ${S}^{z}=\ifmmode\pm\else\textpm\fi{}2/3$ describe well the low-energy excitations around the 1/3 plateau state. The formation of the bound state of the domain walls clearly provides the microscopic mechanism of the cusp singularities and the even-odd behavior in the magnetization curve.We present the microscopic view for the excitations around the 1/3 plateau state of the Ising-like zigzag $\mathrm{XXZ}$ chain. We analyze the low-energy excitations around the plateau with the degenerating perturbation theory from the Ising limit, combined with the Bethe-form wave function. We then find that the domain-wall particles carrying ${S}^{z}=\ifmmode\pm\else\textpm\fi{}1/3$ and its bound state of ${S}^{z}=\ifmmode\pm\else\textpm\fi{}2/3$ describe well the low-energy excitations around the 1/3 plateau state. The formation of the bound state of the domain walls clearly provides the microscopic mechanism of the cusp singularities and the even-odd behavior in the magnetization curve.

arXiv:cond-mat/0307121Physical review. B, Condensed matterDec 23, 200344 citations

M=1\ensuremath{-}\frac{2}{N}

(N=3,4,\dots{})

plateau decays into

N

elementary excitations each carrying a fraction

\frac{1}{N}

of the spin. This fractionalization goes beyond the well-known decay of one magnon into two spinons taking place on top of the

M=0

plateau. Concentrating on the

\frac{1}{3}

plateau

(N=3)

we unravel the microscopic structure of the domain walls which carry fractional spin-

\frac{1}{3}

, both from theory and numerics. These excitations are shown to be noninteracting and should be observable in x-ray and nuclear magnetic resonance experiments.

We demonstrate that domain-wall type excitations carrying the fractional magnetization

S^z=\pm1/3

and their bound state describe the low-energy physics around the 1/3 plateau of the antiferromagnetic zigzag spin chain in the strongly frustrated region. In particular we discuss the relevance of such domain-wall excitations to the characteristic properties of the magnetization curves: the 1/3 plateau accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve.

m=1∕2

. We show that even for purely isotropic Heisenberg interactions, the magnetization curve exhibits a rather complex behavior that can be fully accounted for in terms of simple elementary excitations. The introduction of anisotropic interactions (e.g., Dzyaloshinskii-Moriya interactions) modifies significantly the picture and reveals an essential difference between integer and fractional plateaus. In particular, anisotropic interactions generically open a gap in the region between the plateaus, but we show that this gap closes upon entering fractional plateaus. All of these conclusions, based on analytical arguments, are supported by extensive density matrix renormalization group calculations.

5/2

case confirms the universality of these phenomena across half-integer higher-spin systems. Our results provide detailed insight into how fractionalization and incommensurate condensation govern the spectral properties of frustrated spin chains, offering a unified picture across different spin magnitudes.

We study the

T=0

magnetization of frustrated two-leg spin ladders with arbitrary value of the spin

S

. In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins

S

and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaus. These ratios depend both on the plateau and on the spin. To confirm these results and to investigate the properties of these ladders away from the strong-coupling limit, we have performed extensive density-matrix renormalization-group calculations for $S\ensuremath{\le}2$. For large enough inter-rung couplings, all plateaus simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.

We present the microscopic view for the excitations around the 1/3 plateau state of the Ising-like zigzag

\mathrm{XXZ}

chain. We analyze the low-energy excitations around the plateau with the degenerating perturbation theory from the Ising limit, combined with the Bethe-form wave function. We then find that the domain-wall particles carrying ${S}^{z}=\ifmmode\pm\else\textpm\fi{}1/3$ and its bound state of ${S}^{z}=\ifmmode\pm\else\textpm\fi{}2/3$ describe well the low-energy excitations around the 1/3 plateau state. The formation of the bound state of the domain walls clearly provides the microscopic mechanism of the cusp singularities and the even-odd behavior in the magnetization curve.