Quantum spin dynamics of the one-dimensional planar antiferromagnet

Müller, Gerhard; Thomas, H.; Puga, M. W.; Beck, H. P.

doi:10.1088/0022-3719/14/23/017

Cited by 57 publications

(48 citation statements)

References 34 publications

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“…It is interesting to note that the general shape of S zz (q, ω) for ∆ = −0.1 from (16) is in remarkably good agreement with S zz (q, ω) as obtained in Ref. 19 by a completely different approach. The Hartree-Fock result (16) evaluated at ∆ = −1, on the other hand, has serious deficiencies [15].…”

Section: Green Function Approach To S Zz (Q ω)supporting

confidence: 84%

“…An analytic expression for S xx (q, ω) in the limit ∆ = 0 obtained by a different approach has been given in Ref. 19 including figures of lineshapes [18]. An extension of that approach for S xx (q, ω) and S zz (q, ω) to ∆ > 0 together with a more detailed account of the present calculations including second-order terms in V (q) will be published in due course.…”

Section: Behavior Of S XX (Q ω)mentioning

confidence: 99%

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Excitation spectrum and T=0 dynamics of the one-dimensional planar spin- ferromagnet

Beck

Müller

1982

Solid State Communications

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The T = 0 dynamics of the one-dimenslonal S = 1/2 ferromagnet with planar exchange anisotropy is studied by finite-chaln calculations and a Green function approach. We demonstrate that the excitation spectrum relevant for appropriate low-T inelastic neutron scattering experiments is much more complex than predicted by linear spin-wave theory. It includes two continua and a set of discrete branches. Some of the low-lying excitations predicted by rigorous calculations, on the other hand, are shown to contribute no spectral weight to the T = 0 dynamic structure factor Szz(q, ω). We provide quantitative results for the spectral-weight distribution in Szz(q, ω) at T = 0 from bound states and continuum states, including a detailed analysis of the singularity in Szz(q, ω) at the lower band edge. Further evidence is found for the prediction that some T = 0 critical properties of the planar S = 1/2 ferro-and antiferromagnet are governed by exponents which depend continuously on the planar anisotropy.

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Section: Green Function Approach To S Zz (Q ω)supporting

confidence: 84%

Section: Behavior Of S XX (Q ω)mentioning

confidence: 99%

Excitation spectrum and T=0 dynamics of the one-dimensional planar spin- ferromagnet

Beck

Müller

1982

Solid State Communications

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“…[16]). It has the advantage that the fluctuation function Φ µµ (q, ω), the Fourier transform of (S µ l (t) − S µ l )(S µ l − S µ l ) can be written in the simple form…”

Section: Role Of H N In the Classical Limitmentioning

confidence: 99%

“…An equivalent but even simpler way [16,17] is to use the fact that the first frequency moment of Φ µµ (q, ω)…”

Section: Role Of H N In the Classical Limitmentioning

confidence: 99%

Antiferromagnetic long-range order in the anisotropic quantum spin chain

Kurmann

Thomas

Müller

1982

Physica A: Statistical Mechanics and its Applications

227

332

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This is a study of the ground-state properties of the one-dimensional spin-s (1/2 < s < ∞) anisotropic XY Z antiferromagnet in a magnetic field of arbitrary direction. It provides the first rigorous results for the general case of this model in non-zero field. By exact calculations we find the existence of an ellipsoidal surface h = h N in field space where the ground state is of the classical two-sublattice Néel type with non-zero antiferromagnetic long-range order. At h N there are no correlated quantum fluctuations. We give upper and lower bounds for the critical field hc where antiferromagnetic long-range order is suppressed by the field. The zero-temperature phase diagrams are discussed for a few representative cases.

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“…Only single particle-hole excitations contribute, the exact structure factor being proportional to their density of states. For ∆ > 0, this picture breaks down 7,8 due to nonperturbative effects. It is the purpose of this paper to track in detail the effects of 'turning on' interactions on the spinon quasiparticles and their ability to carry correlations, throughout the gapless antiferromagnetic regime 0 ≤ ∆ ≤ 1.…”

mentioning

confidence: 97%

Tracking the Effects of Interactions on Spinons in Gapless Heisenberg Chains

et al. 2011

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We consider the effects of interactions on spinon excitations in Heisenberg spin-1/2 chains. We compute the exact two-spinon part of the longitudinal structure factor of the infinite chain in zero field for all values of anisotropy in the gapless antiferromagnetic regime, via an exact algebraic approach. Our results allow us to quantitatively describe the behaviour of these fundamental excitations throughout the observable continuum, for cases ranging from free to fully coupled chains, thereby explicitly mapping the effects of 'turning on the interactions' in a strongly-correlated system.Interactions in one-dimensional (1d) systems are known to overwhelm constituent particles, leading to a collective quantum liquid state with low-energy excitations described by the theory of Tomonaga-Luttinger liquids 1 . While the 'universal' physics of 1d systems is phenomenologically well understood 2 , it almost always remains impossible to precisely track the effects of 'turning on the interactions' on the constituent particles, as one does for Fermi liquids 3 (where bare fermions are adiabatically connected to Landau quasiparticles). In this respect, our general understanding of 1d systems can benefit from nonperturbative solutions of microscopic models, a fundamental example being the Heisenberg spin-1/2 anisotropic chain 4,5 , whose Hamiltonian isThis system is a Tomogana-Luttinger liquid for anisotropy values ∆ in the range −1 < ∆ ≤ 1 (in zero field, with J > 0). Its fundamental excitations are spinons 6 : spin-1/2 fractionalized objects which can be viewed as domain walls dressed by quantum fluctuations.A way to probe the nature of excitations is to determine how they carry observable correlations, an interesting example here being the longitudinal structure factorAt ∆ = 0, this can be written as a density correlator of Jordan-Wigner fermions. Only single particle-hole excitations contribute, the exact structure factor being proportional to their density of states. For ∆ > 0, this picture breaks down 7,8 due to nonperturbative effects. It is the purpose of this paper to track in detail the effects of 'turning on' interactions on the spinon quasiparticles and their ability to carry correlations, throughout the gapless antiferromagnetic regime 0 ≤ ∆ ≤ 1. Systems in this regime can be realized and studied experimentally (for fixed anisotropy) in spin ladder compounds 9-11 or (in principle for generic anisotropy) using optical lattices 12 . Focusing on zero temperature, we will compute the exact two-spinon contribution to (2) directly in the thermodynamic limit N → ∞, using an adaptation of the 'vertex operator approach' 13 . Our results provide a strict lower bound and (for practical purposes) an extremely accurate representation for the complete correlator of the infinite system (more that 99% for anisotropies below 0.5) throughout the observable excitation continuum. They provide a robust benchmark for assessing the lineshapes obtained for finite systems directly from integrability 14,15 or using variants of the density...

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Quantum spin dynamics of the one-dimensional planar antiferromagnet

Cited by 57 publications

References 34 publications

Excitation spectrum and T=0 dynamics of the one-dimensional planar spin- ferromagnet

Excitation spectrum and T=0 dynamics of the one-dimensional planar spin- ferromagnet

Antiferromagnetic long-range order in the anisotropic quantum spin chain

Tracking the Effects of Interactions on Spinons in Gapless Heisenberg Chains

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