Sine-Gordon low-energy effective theory for copper benzoate

Eßler, Fabian H. L.

doi:10.1103/physrevb.59.14376

Cited by 74 publications

(83 citation statements)

References 76 publications

(78 reference statements)

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“…[20][21][22] Since there exist one soliton, one antisoliton and three breathers for 0 q < , the soliton contribution is doubly counted in C SG . To obtain the soliton mass M s , we fit C p ¼ C SG þ bT 3 to the specific heat data for T < 0:4M s =k B .…”

Section: )mentioning

confidence: 99%

Thermodynamic Properties and Elementary Excitations in Quantum Sine-Gordon Spin System KCuGaF₆

et al. 2007

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Thermodynamic properties and elementary excitations in S ¼ 1=2 one-dimensional Heisenberg antiferromagnet KCuGaF 6 were investigated by magnetic susceptibility, specific heat and ESR measurements. Due to the Dzyaloshinsky-Moriya interaction with alternating D-vectors and/or the staggered g-tensor, the staggered magnetic field is induced when subjected to external magnetic field. Specific heat in magnetic field clearly shows the formation of excitation gap, which is attributed to the staggered magnetic field. The specific heat data was analyzed on the basis of the quantum sine-Gordon (SG) model. We observed many ESR modes including one soliton and three breather excitations characteristic of the quantum SG model. Studies of antiferromagnetic Heisenberg chain (AFHC) have long history. For S ¼ 1=2 uniform AFHC, the ground state, thermodynamic properties and magnetic excitations are well understood with the help of exact solutions [1][2][3][4] and accurate analytical and numerical calculations.5-8) These theoretical results demonstrate the importance of the quantum fluctuation characteristic of low-dimensional systems. In particular, exact result of the magnetic excitations in an external magnetic field H is qualitatively different from the results of the linear spin wave theory. The gapless excitations occur at incommensurate wave vectors q ¼ AE2mðHÞ and AE 2mðHÞ in addition to at q ¼ 0 and , where mðHÞ is the magnetization per site in the unit of g B . 4)Recently, the physics of S ¼ 1=2 AFHC in staggered magnetic field induced by the external magnetic field has been attracting considerable attention.9,10) The model Hamiltonian of such system is written aswhere h is the staggered field perpendicular to the external field H and is given by h ¼ c s H. This magnetic model is actualized in some S ¼ 1=2 AFHC systems such as (H 2 O) 2 (PM = pyrimidine). 15,16) The staggered field originates from the alternating g-tensor and the antisymmetric interaction of the Dzyaloshinsky-Moriya (DM) type with the alternating D vector. In these compounds, the fieldinduced gap ÁðHÞ almost proportional to H 2=3 was commonly observed. This field dependence of the gap cannot be explained by the linear spin wave theory, which derives ÁðHÞ / H 1=2 . Using the field theoretical approach, Oshikawa and Affleck 9,10) argued that the model (1) can be mapped onto the quantum sine-Gordon (SG) model with Lagrangian density L ¼ ð1=2Þð@ Þ þ hC cosð2R Þ, where is a canonical Bose field, is the dual field, R is the compactification radius and C is a coupling constant, and that the gap is expressed as ÁðhÞ ' 1:85Jðg B h=JÞ 2=3 lnðJ=g B hÞ 1=6 . Their result is in agreement with experimental results. [11][12][13][14][15][16] In the above-mentioned compounds, the exchange interaction is order of 10 K and the proportional coefficient is rather small, c s ¼ 0:08.13,16) For the comprehensive understanding of the systems described by the model (1), new compounds having different interaction constants are necessary. In this letter, we show that the static and d...

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Section: )mentioning

confidence: 99%

Thermodynamic Properties and Elementary Excitations in Quantum Sine-Gordon Spin System KCuGaF₆

et al. 2007

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“…The sine-Gordon quantum field theory [8][9][10] applied for this model predicts that the elementary excitation spectrum is to be formed by solitons and their multiple bound states (breathers) with an energy gap ∆ ∝ H formed by the first breather mode [11,12]. Such a sineGordon spin model has been found to be realized in a number of compounds [13][14][15][16][17][18].…”

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confidence: 99%

“…[6]), and, in particular, their highfield behavior. A Heisenberg spin-1/2 chain with exchange interaction J and DM interaction (or alternating g-tensor) in a field H can be mapped to a simple Heisenberg chain with a staggered transverse field h ∝ H [8][9][10], described by the effective spin Hamiltonian…”

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confidence: 99%

Field-induced gap in a quantum spin-12chain in a strong magnetic field

et al. 2011

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Magnetic excitations in copper pyrimidine dinitrate, a spin-1/2 antiferromagnetic chain with alternating g-tensor and Dzyaloshinskii-Moriya interactions that exhibits a field-induced spin gap, are probed by means of pulsed-field electron spin resonance spectroscopy. In particular, we report on a minimum of the gap in the vicinity of the saturation field Hsat = 48.5 T associated with a transition from the sine-Gordon region (with soliton-breather elementary excitations) to a spin-polarized state (with magnon excitations). This interpretation is fully confirmed by the quantitative agreement over the entire field range of the experimental data with the DMRG calculations for spin-1/2 Heisenberg chain with a staggered transverse field.PACS numbers: 75.40. Gb, 75.10.Jm Introduction.-Due to recent progress in theory and the growing number of physical realizations, lowdimensional quantum magnets continue to receive a considerable amount of attention. They serve as model systems for investigating numerous fascinating phenomena in materials with cooperative ground states, in particular, induced by high magnetic fields. The way a magnetic field changes the ground-state properties and, correspondingly, the low-energy excitation spectrum of lowdimensional magnets is one of the fundamental aspects in quantum magnetism. For example, the zero-field ground state of an isotropic S = 1/2 Heisenberg antiferromagnetic (AF) chain with uniform nearest-neighbor exchange coupling is a spin singlet, and its spin dynamics is determined by a gapless two-particle continuum of fractional S = 1/2 excitations, called spinons. Application of an external magnetic field H leads to a pronounced rearrangement of the excitation spectrum, making the soft modes incommensurate [1, 2] but leaving the spinon continuum gapless. However, in a fully spin-polarized phase, H > H sat , the excitation spectrum is gapped and dominated by ordinary spin waves (magnons). The low-energy excitation spectrum of such an ideal isotropic Heisenberg S = 1/2 chain can be described in terms of an effective free massless boson theory [3][4][5].The presence of additional interactions such as Dzyaloshinskii-Moriya (DM) interaction [7] can significantly alter the physical properties of such spin systems (see for instance Ref.[6]), and, in particular, their highfield behavior. A Heisenberg spin-1/2 chain with exchange interaction J and DM interaction (or alternating g-tensor) in a field H can be mapped to a simple Heisenberg chain with a staggered transverse field h ∝ H [8-10], described by the effective spin Hamiltonian

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“…It has already known 31,32,33,34 that the same type of the band splitting appears in the spin-1 2 AF chain with the staggered field, when the field is sufficiently small: the effective theory of such a spin-1 2 chain is a sine-Gordon model, which low-energy spectrum consists of the massive soliton, the antisoliton (these two are degenerate) and the breather (bound state of the soliton and antisoliton). Therefore, the band splitting of two and single ones may be a universal feature in 1D AF spin systems with an alternating field around the isotropic [SU (2) …”

Section: Summary and Discussionmentioning

confidence: 95%

“…Staggered magnetic fields have been investigated recently. 31,32,33,34,35,36,37,38,39,40,41,42,43,44 Actually such fields are present in real magnets, 36,37,45,46,47,48,49,50,51 and their origins have been explained. 32,42 One will see that these four terms are congenial to the NLSM method.…”

Section: Introductionmentioning

confidence: 99%

N-leg integer-spin ladders and tubes in commensurate external fields: Nonlinear sigma model approach

Sato

2005

Phys. Rev. B

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We investigate the low-energy properties, especially the low-energy excitation structures, of N -leg integer-spin ladders and tubes with an antiferromagnetic (AF) intrachain coupling. In the odd-leg tubes, the AF rung coupling causes the frustration. To treat all ladders and tubes systematically, we apply Sénéchal's method [Phys. Rev. B 52, 15319 (1995)], based on the nonlinear sigma model, together with a saddle-point approximation. This strategy is valid in the weak interchain (rung) coupling regime. We show that all frustrated tubes possess six-fold degenerate spin-1 magnon bands, as the lowest excitations, while other ladders and tubes have a standard triply degenerate bands. We also consider effects of four kinds of Zeeman terms: uniform, staggered only along the rung, only along the chain, or both directions. The above prediction of the no-field case implies that a sufficiently strong uniform field yields a two-component Tomonaga-Luttinger liquid (TLL) due to the condensation of doubly degenerate lowest magnons in frustrated tubes. In contrast, the field induces a standard one-component TLL in all other systems. This is supported by symmetry and bosonization arguments based on the Ginzburg-Landau theory. The bosonization also suggests that the two-component TLL vanishes and a one-component TLL appears, when the uniform field becomes larger for the second lowest magnon bands to touch the zero-energy line. This transition could be observed as a cusp singularity in the magnetization process. When the field is staggered only along the rung direction, it is implied that the lowest doubly-degenerate bands fall down with the field increasing in all systems. For final two cases where the fields are staggered along the chain, it is showed that at least in the weak rung-coupling region, the lowest-excitation gap grows with the field increasing, and no critical phenomena occurs. Furthermore, for the ladders of the final two cases, we predict that the inhomogeneous magnetization along the rung occurs, and the frustration between the field and the rung coupling can induce the magnetization pointing to the opposite direction to the field. All the analyses suggest that the emergence of the doubly degenerate transverse magnons and the single longitudinal one is universal for the one-dimensional AF spin systems with a weak staggered field.

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Sine-Gordon low-energy effective theory for copper benzoate

Abstract: Specific heat data for the quasi one dimensional quantum magnet Copper Benzoate (Cu(C6D5COO)2 · 3D2O) is analyzed in the framework of an effective low-energy description in terms of a Sine-Gordon theory.

Cited by 74 publications

References 76 publications

Thermodynamic Properties and Elementary Excitations in Quantum Sine-Gordon Spin System KCuGaF₆

Thermodynamic Properties and Elementary Excitations in Quantum Sine-Gordon Spin System KCuGaF₆

Field-induced gap in a quantum spin-12chain in a strong magnetic field

N-leg integer-spin ladders and tubes in commensurate external fields: Nonlinear sigma model approach

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Sine-Gordon low-energy effective theory for copper benzoate

Abstract: Specific heat data for the quasi one dimensional quantum magnet Copper Benzoate (Cu(C6D5COO)2 · 3D2O) is analyzed in the framework of an effective low-energy description in terms of a Sine-Gordon theory.

Cited by 74 publications

References 76 publications

Thermodynamic Properties and Elementary Excitations in Quantum Sine-Gordon Spin System KCuGaF6

Thermodynamic Properties and Elementary Excitations in Quantum Sine-Gordon Spin System KCuGaF6

Field-induced gap in a quantum spin-12chain in a strong magnetic field

N-leg integer-spin ladders and tubes in commensurate external fields: Nonlinear sigma model approach

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Product

Resources

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Thermodynamic Properties and Elementary Excitations in Quantum Sine-Gordon Spin System KCuGaF₆

Thermodynamic Properties and Elementary Excitations in Quantum Sine-Gordon Spin System KCuGaF₆