Effective Field Theory Approach to Ferromagnets and Antiferromagnets in Crystalline Solids

Román, José Marı́a; Soto, Joan

doi:10.1142/s0217979299000655

Cited by 47 publications

(95 citation statements)

References 22 publications

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“…It is, therefore, useful to recall the breaking of spin-rotational symmetry O(3) to O(2) in infinite ferromagnets [5,7,9]. In the ground state, all spins point in the same direction, violating the spin-rotational symmetry of the Hamiltonian.…”

Section: Emergent Breaking Of Rotational Symmetrymentioning

confidence: 99%

“…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%

“…Our procedure is patterned after the case of the infinite ferromagnet [5,7,10]. We generalize the expression for unitary transformations in the coset space by including purely time-dependent variables.…”

Section: Introductionmentioning

confidence: 99%

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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: Emergent Breaking Of Rotational Symmetrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effective field theory for finite systems with spontaneously broken symmetry

Papenbrock

Weidenmüller

2014

Phys. Rev. C

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“…In order to make this paper self-contained, in this section we review the effective theory for magnons and holes constructed in [70,71] which is based on the pure magnon effective theory of [10,13,23,30,35,65,66,67,68].…”

Section: Systematic Low-energy Effective Field Theory For Magnons Andmentioning

confidence: 99%

Homogeneous versus spiral phases of hole-doped antiferromagnets: A systematic effective field theory investigation

et al. 2007

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Using the low-energy effective field theory for magnons and holes -the condensed matter analog of baryon chiral perturbation theory for pions and nucleons in QCD -we study different phases of doped antiferromagnets. We systematically investigate configurations of the staggered magnetization that provide a constant background field for doped holes. The most general configuration of this type is either constant itself or it represents a spiral in the staggered magnetization. Depending on the values of the low-energy parameters, a homogeneous phase, a spiral phase, or an inhomogeneous phase is energetically favored. The reduction of the staggered magnetization upon doping is also investigated.

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“…Analogous to chiral perturbation theory for the Nambu-Goldstone pions in QCD [46], a systematic low-energy effective theory for magnons has been developed in [55,56,57,58,59,60,61,62,63]. In order to couple charge carriers to the magnons, a nonlinear realization of the SU(2) s symmetry has been constructed in [47].…”

Section: Symmetries Of Microscopic Modelsmentioning

confidence: 99%

Two-hole bound states from a systematic low-energy effective field theory for magnons and holes in an antiferromagnet

et al. 2006

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Identifying the correct low-energy effective theory for magnons and holes in an antiferromagnet has remained an open problem for a long time. In analogy to the effective theory for pions and nucleons in QCD, based on a symmetry analysis of Hubbard and t-J-type models, we construct a systematic low-energy effective field theory for magnons and holes located inside pockets centered at lattice momenta (±). The effective theory is based on a nonlinear realization of the spontaneously broken spin symmetry and makes model-independent universal predictions for the entire class of lightly doped antiferromagnetic precursors of high-temperature superconductors. The predictions of the effective theory are exact, order by order in a systematic low-energy expansion. We derive the one-magnon exchange potentials between two holes in an otherwise undoped system. Remarkably, in some cases the corresponding two-hole Schrödinger equations can even be solved analytically. The resulting bound states have d-wave characteristics. The ground state wave function of two holes residing in different hole pockets has a d x 2 −y 2 -like symmetry, while for two holes in the same pocket the symmetry resembles d xy .

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Effective Field Theory Approach to Ferromagnets and Antiferromagnets in Crystalline Solids

Cited by 47 publications

References 22 publications

Effective field theory for finite systems with spontaneously broken symmetry

Effective field theory for finite systems with spontaneously broken symmetry

Homogeneous versus spiral phases of hole-doped antiferromagnets: A systematic effective field theory investigation

Two-hole bound states from a systematic low-energy effective field theory for magnons and holes in an antiferromagnet

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