Exact two-spinon dynamical correlation function of the one-dimensional Heisenberg model

Bougourzi, A. H.; Couture, M; Kacir, M.

doi:10.1103/physrevb.54.r12669

Cited by 89 publications

(136 citation statements)

References 13 publications

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“…͑5.1͒ and ͑6.2͒ disappear in the isotropic limit. The results presented previously for the isotropic case 30,31 can be recovered from the more general result presented here if we replace the spectral parameter ␤ in Eq. ͑2.7͒ by the scaled spectral parameter ␣ϭϪ␤ /2KЈ and then take the limit q→Ϫ1 Ϫ .…”

Section: ͑611͒mentioning

confidence: 55%

“…29 The algebraic analysis 23 operates in the massive phase stabilized by Néel long-range order at ⌬ϽϪ1, but the isotropic limit ⌬→Ϫ1 Ϫ can be performed meaningfully at various stages of the calculation and thus yields equivalent results for the ͑massless͒ Heisenberg antiferromagnet. 30,31 In this paper we infer from the diverse ingredients now accessible via the Bethe ansatz and the algebraic analysis an explicit expression for the exact two-spinon part of the dynamic spin structure factor…”

Section: Introductionmentioning

confidence: 99%

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Exact two-spinon dynamic structure factor of the one-dimensionals=12Heisenberg-Ising antiferromagnet

1998

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Exact two-spinon dynamic structure factor of the one-dimensional s=1/2 HeisenbergIsing antiferromagnet. Physical Review B, 57(1998) The exact two-spinon part of the dynamic spin structure factor S xx (Q, ) for the one-dimensional sϭ1/2, XXZ model at Tϭ0 in the antiferromagnetically ordered phase is calculated using recent advances in the algebraic analysis based on ͑infinite-dimensional͒ quantum group symmetries of this model and the related vertex models. The two-spinon excitations form a two-parameter continuum consisting of two partly overlapping sheets in (Q, ) space. The spectral threshold has a smooth maximum at the Brillouin zone boundary (Qϭ /2) and a smooth minimum with a gap at the zone center (Qϭ0). The two-spinon density of states has square-root divergences at the lower and upper continuum boundaries. For the two-spinon transition rates, the two regimes 0рQϽQ ͑near the zone center͒ and Q ϽQр /2 ͑near the zone boundary͒ must be distinguished, where Q →0 in the Heisenberg limit and Q → /2 in the Ising limit. In the regime Q ϽQр /2, the two-spinon transition rates relevant for S xx (Q, ) are finite at the lower boundary of each sheet, decrease monotonically with increasing , and approach zero linearly at the upper boundary. The resulting two-spinon part of S xx (Q, ) is then square-root divergent at the spectral threshold and vanishes in a square-root cusp at the upper boundary. In the regime 0ϽQ р /2, in contrast, the two-spinon transition rates have a smooth maximum inside the continuum and vanish linearly at either boundary. In the associated two-spinon line shapes of S xx (Q, ), the linear cusps at the continuum boundaries are replaced by square-root cusps. Existing perturbation studies have been unable to capture the physics of the regime Q ϽQр /2. However, their line-shape predictions for the regime 0рQϽQ are in good agreement with the exact results if the anisotropy is very strong. For weak anisotropies, the exact line shapes are more asymmetric. ͓S0163-1829͑98͒04717-1͔

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Section: ͑611͒mentioning

confidence: 55%

Section: Introductionmentioning

confidence: 99%

Exact two-spinon dynamic structure factor of the one-dimensionals=12Heisenberg-Ising antiferromagnet

1998

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“…where M α are given by (11). In order to compare theoretical predictions based on the SGM with the specific heat data of [21] we need the free energy at "intermediate" temperatures and thus have to resort to a numerical solution of (14) by iteration.…”

Section: Sine-gordon Thermodynamicsmentioning

confidence: 99%

“…Starting with Bethe's seminal work [2] a host of exact results have been obtained for ground state properties [3], magnetic susceptibility [4], thermodynamics [5,6], excitation spectrum [7,8] and correlation functions [9][10][11][12]. From the point of view of standard spin wave theory, which is highly successful for "three dimensional" materials, the findings of the these investigations were rather unusual.…”

mentioning

confidence: 99%

Sine-Gordon low-energy effective theory for copper benzoate

Eßler

1999

Phys. Rev. B

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“…14͑a͒. For sufficiently strong exchange coupling, the function S zz ( , ) t-J will be characterized by a strong, i.e., nonintegrable infrared divergence, ϳͱϪln / , 43 which characterizes the order-parameter fluctuations of the 1D sϭ1/2 XXX antiferromagnet. Figure 14͑b͒ shows the gradual change in line shape and shift in peak position of the function S zz ( /2, ) t-J in the phase-separated state.…”

Section: Spin Dynamics "T-j Model…mentioning

confidence: 99%

Charge and spin dynamics in the one-dimensional t-Jzand t-J models

et al. 1997

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The impact of the spin-flip terms on the ͑static and dynamic͒ charge and spin correlations in the Luttingerliquid ground state of the one-dimensional ͑1D͒ t-J model is assessed by comparison with the same quantities in the 1D t-J z model, where spin-flip terms are absent. We employ the recursion method combined with a weak-coupling or a strong-coupling continued-fraction analysis. At J z /tϭ0 ϩ we use the Pfaffian representation of dynamic spin correlations. The changing nature of the dynamically relevant charge and spin excitations on approach of the transition to phase separation is investigated in detail. At the transition point, the t-J z ground state has zero ͑static͒ charge correlations and very short-ranged ͑static͒ spin correlations, whereas the t-J ground state is critical. The t-J z charge excitations ͑but not the spin excitations͒ at the transition have a single-mode nature, whereas charge and spin excitations have a complicated structure in the t-J model. A major transformation of the t-J spin excitations takes place between two distinct regimes within the Luttingerliquid phase, while the t-J z spin excitations are found to change much more gradually. In the t-J z model, phase separation is accompanied by Néel long-range order, caused by the condensation of electron clusters with an already existing alternating up-down spin configuration ͑topological long-range order͒. In the t-J model, by contrast, the spin-flip processes in the exchange coupling are responsible for continued strong spin fluctuations ͑dominated by two-spinon excitations͒ in the phase-separated state. ͓S0163-1829͑97͒06210-3͔

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Exact two-spinon dynamical correlation function of the one-dimensional Heisenberg model

Cited by 89 publications

References 13 publications

Exact two-spinon dynamic structure factor of the one-dimensionals=12Heisenberg-Ising antiferromagnet

Exact two-spinon dynamic structure factor of the one-dimensionals=12Heisenberg-Ising antiferromagnet

Sine-Gordon low-energy effective theory for copper benzoate

Charge and spin dynamics in the one-dimensional t-Jzand t-J models

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