Spin-wave scattering in the effective Lagrangian perspective

Hofmann, Christoph P.

doi:10.1103/physrevb.60.388

Cited by 68 publications

(98 citation statements)

References 45 publications

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“…Examples for spontaneous symmetry breaking are the breaking of spin-rotational symmetry in a ferromagnet, the breaking of translational symmetry in a crystal lattice, and the breaking of chiral symmetry in quantum chromodynamics (QCD). In these examples, the Nambu-Goldstone modes are magnons, phonons, and pions, respectively, and EFTs have been developed for all these cases [4][5][6][7][8][9][10], see Refs. [11,12] for reviews.…”

Section: Introductionmentioning

confidence: 99%

Effective field theory for finite systems with spontaneously broken symmetry

Papenbrock

Weidenmüller

2014

Phys. Rev. C

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We extend effective field theory to the case of spontaneous symmetry breaking in genuinely finite quantum systems such as small superfluid systems, molecules or atomic nuclei, and focus on deformed nuclei. In finite superfluids, symmetry arguments alone relate the spectra of systems with different particle numbers. For systems with non-spherical intrinsic ground states such as atomic nuclei or molecules, symmetry arguments alone yield the universal features of the low-lying excitations as vibrations that are the heads of rotational bands. The low-lying excitations in deformed nuclei differ from those in molecules because of symmetry properties caused by pairing.

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Section: Introductionmentioning

confidence: 99%

Effective field theory for finite systems with spontaneously broken symmetry

Papenbrock

Weidenmüller

2014

Phys. Rev. C

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“…are the Goldstone bosons of a spontaneously broken spin symmetry SU (2)s -^ U{\)s, while phonons emerge due to a spontaneously broken translation symmetry, to name just a few. For these systems effective Lagrangians have been constructed and various applications have been considered [6,7,8].…”

Section: Motivationmentioning

confidence: 99%

“…We also assumed that four-fermion contact interactions -not displayed in Eqs. (8) and (10) -are weak and took them into account perturbatively -for details seeRefs. [ll, 17].…”

Section: Spiral Phases In Weakly Doped Antiferromagnetsmentioning

confidence: 99%

On the Condensed Matter Analog of Baryon Chiral Perturbation Theory

Brügger¹,

Hofmann²,

Kämpfer³

et al. 2009

PARTICLES AND FIELDS: Proceedings of the XIII Mexican School of Particles and Fields

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It is shown that baryon chiral perturbation theory, i.e., the low-energy effective theory for pions and nucleons in quantum chromodynamics, has its condensed matter analog: A low-energy effective theory describing magnons as well as holes (or electrons) doped into antiferromagnets. We briefly present a symmetry analysis of the Hubbard and t-J-typs models, and review the construction of the leading terms in the effective Lagrangian. As a nontrivial application we study differentphases of hole-and electron-doped antiferromagnets -in particular, we investigate whether a so-called spiral phase with an inhomogeneous staggered magnetization (order parameter) may be stable. We would like to emphasize that the effective theory is universal and makes model-independent predictions for a large class of systems, whereas the material-specific properties enter the effective theory only through the numerical values of a few low-energy parameters.

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“…(14). General symmetry arguments [8] suggest that this suppression survives when we take into account the renormalization of the staggered spin fluctuations by the ferromagnetic ones. We have explicitly verified this within the Hartree-Fock approximation, where the two-body part in Eq.…”

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confidence: 99%

“…The interactionĤ int involves at least four boson operators and higher powers of the small parameter 1/S, so that for large S it is reasonable to treatĤ int perturbatively. However, as we discuss in more detail below, in momentum space the vertices ofĤ int have a complicated non-analytic structure for small momenta [5][6][7], so that the expected supression of the interaction between long-wavelength Goldstone modes [8] is not manifest in this approach. On the other hand, in the calculation of physical quantities that are dominated by staggered spin-fluctuations the leading momentum-dependence of the vertices eventually cancels [9].…”

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confidence: 99%

Spin-wave interactions in quantum antiferromagnets

Hasselmann

Kopietz

2006

Europhys. Lett.

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PACS. 75.10.Jm -Quantized spin models. PACS. 75.30.Ds -Spin waves.Abstract. -We study spin-wave interactions in quantum antiferromagnets by expressing the usual magnon annihilation and creation operators in terms of Hermitian field operators representing transverse staggered and ferromagnetic spin fluctuations. In this parameterization, which was anticipated by Anderson in 1952, the two-body interaction vertex between staggered spin fluctuations vanishes at long wavelengths. We derive a new effective action for the staggered fluctuations only by tracing out the ferromagnetic fluctuations. To one loop order, the renormalization group flow agrees with the nonlinear-σ-model approach.The spin-wave approach to quantum Heisenberg antiferromagnets, which was pioneered by Anderson [1] and Kubo [2] more than half a century ago, is still one of the most powerful methods to calculate the low-temperature properties of ordered magnets. In this approach, the components of the quantum-mechanical spin-operators S i are expressed in terms of canonical boson operators b i using the Holstein-Primakoff [3] or the Dyson-Maleev [4] transformation. The spin-S antiferromagnetic Heisenberg Hamiltoniancan then be written as a bosonic many-body HamiltonianĤ = −DN JS 2 +Ĥ 2 +Ĥ int , where the quadratic part isĤThe spins are assumed here to be localized at the sites r i of a D-dimensional hypercubic lattice with lattice spacing a. The lattice is bipartite, with sublattices labelled A and B. We also assume J ij = J > 0 for all pairs of nearest neighbors and J ij = 0 otherwise. The interactionĤ int involves at least four boson operators and higher powers of the small parameter 1/S, so that for large S it is reasonable to treatĤ int perturbatively. However, as we discuss in more detail below, in momentum space the vertices ofĤ int have a complicated non-analytic structure for small momenta [5][6][7], so that the expected supression of the interaction between long-wavelength Goldstone modes [8] is not manifest in this approach. On the other hand, in the calculation of physical quantities that are dominated by staggered spin-fluctuations the leading momentum-dependence of the vertices eventually cancels [9].c EDP Sciences

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Spin-wave scattering in the effective Lagrangian perspective

Cited by 68 publications

References 45 publications

Effective field theory for finite systems with spontaneously broken symmetry

Effective field theory for finite systems with spontaneously broken symmetry

On the Condensed Matter Analog of Baryon Chiral Perturbation Theory

Spin-wave interactions in quantum antiferromagnets

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