Magnon-mediated binding between holes in an antiferromagnet

Brügger, Christoph; Kämpfer, Florian; Wiese, U.‐J.

doi:10.1140/epjb/e2006-00398-y

Cited by 26 publications

(41 citation statements)

References 46 publications

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“…In this section we calculate the one-magnon exchange potentials between holes and we solve the corresponding two-hole Schrödinger equations. The one-magnon exchange potentials as well as the solution of the Schrödinger equation for a hole pair of flavors α and β were already discussed in [79]. Here we present a more detailed derivation of these results and we extend the discussion to hole pairs of the same flavor.…”

Section: Magnon-mediated Binding Between Holesmentioning

confidence: 73%

“…The location of the hole pockets has an important effect on the dynamics and implies d-wave characteristics of hole pairs. Using the methods described in this paper, analogous to applications of baryon chiral perturbation theory to few-nucleon systems [69,70,71,72,73,74,75,76,77,78], we have recently investigated magnon-mediated binding between two holes residing in two different hole pockets [79]. Here we discuss these issues in more detail and we extend the investigation to a pair of holes in the same pocket.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Magnon-mediated Binding Between Holesmentioning

confidence: 73%

Section: Introductionmentioning

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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“…In particular, using the effective theory, we have shown that the one-magnon exchange potential between two isolated holes gives rise to binding with d-wave characteristics [71,76]. In a spiral phase the exchange of spiral phonons (i.e.…”

Section: Discussionmentioning

confidence: 97%

“…Recently, we have used the effective theory to derive the magnon-mediated forces between two isolated holes in an otherwise undoped system [71,76]. Remarkably, the Schrödinger equation corresponding to the one-magnon exchange potential can be solved analytically and gives rise to an infinite number of bound states.…”

Section: Introductionmentioning

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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“…Motivated by the success of baryon chiral perturbation theory for QCD, a systematic low-energy effective field theory for magnons and holes in an antiferromagnet on the square lattice was constructed in [13,14]. This theory has been used in a detailed analysis of twohole states bound by one-magnon exchange [14,15] as well as of spiral phases in the staggered magnetization [16], which are a condensed matter analog of pion condensation in dense nuclear matter. The systematic effective field theory investigations have also been extended to electron-…”

Section: Effective Field Theory For Holes and Magnonsmentioning

confidence: 99%

Rotor Spectra, Berry Phases, and Monopole Fields: from Antiferromagnets to QCD

Wiese¹

2009

Proceedings of the XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008)

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Nonrelativistic electrons hopping on the honeycomb lattice of graphene emerge as massless Dirac fermions. When the on-site repulsion between electrons on a honeycomb lattice exceeds a critical value, as it is the case for the dehydrated precursor of the high-temperature superconductor Na 2 CoO 2 × yH 2 O, the system spontaneously breaks its SU(2) s spin symmetry and becomes an antiferromagnet. The emergence of antiferromagnetism is analogous to the spontaneous breakdown of the SU(2) L × SU(2) R chiral symmetry in QCD. Just as the low-energy physics of pions and nucleons is described by baryon chiral perturbation theory, magnons and holes in an antiferromagnet are also described by a systematic low-energy effective theory. Both the chiral condensate in QCD and the staggered magnetization in an antiferromagnet act as a quantum mechanical rotor when the theory is put in a finite volume. When a nucleon is propagating through the QCD vacuum or when a hole is doped into an antiferromagnet, a Berry phase arises from a geometric monopole gauge field and the angular momentum of the rotor is quantized in half-integer units. The finite-size effects of the rotor spectrum depend on the low-energy parameters of the corresponding effective theories.

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Magnon-mediated binding between holes in an antiferromagnet

Cited by 26 publications

References 46 publications

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

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

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

Rotor Spectra, Berry Phases, and Monopole Fields: from Antiferromagnets to QCD

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