Effective Heisenberg Model and Exchange Interaction for Strongly Correlated Systems

Stepanov, E. A.; Brener, S.; Krien, Friedrich; Harland, Malte; Lichtenstein, A. I.; Katsnelson, M. I.

doi:10.1103/physrevlett.121.037204

Cited by 43 publications

(78 citation statements)

References 74 publications

(181 reference statements)

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“…The problem of collective excitations in cuprates is addressed here using the Dual Boson theory [29,30]. The magnetic susceptibility in the ladder DB approximation is given by the following relation [33] X ladd…”

Section: Methodsmentioning

confidence: 99%

Quantum spin fluctuations and evolution of electronic structure in cuprates

et al. 2018

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Correlation effects in CuO 2 layers give rise to a complicated landscape of collective excitations in high-T c cuprates. Their description requires an accurate account for electronic fluctuations at a very broad energy range and remains a challenge for the theory. Particularly, there is no conventional explanation of the experimentally observed "resonant" antiferromagnetic mode, which is often considered to be a mediator of superconductivity. Here we model spin excitations of the hole-doped cuprates in the paramagnetic regime and show that this antiferromagnetic mode is associated with electronic transitions between anti-nodal X and Y points of the quasiparticle band that is pinned to the Fermi level. We observe that upon doping of 7-12% the electronic spectral weight redistribution leads to the formation of a very stable quasiparticle dispersion due to strong correlation effects. The reconstruction of the Fermi surface results in a flattening of the quasiparticle band at the vicinity of the nodal MΓ/2 point, accompanied by a high density of charge carriers. Collective excitations of electrons between the nodal MΓ/2 and XM/2 points form the additional magnetic holes state in magnetic spectrum, which protects the antiferromagnetic fluctuation. Further investigation of the evolution of spin fluctuations with the temperature and doping allowed us to observe the incipience of the antiferromagnetic ordering already in the paramagnetic regime above the transition temperature. Additionally, apart from the most intensive low-energy magnetic excitations, the magnetic spectrum reveals less intensive collective spin fluctuations that correspond to electronic processes between peaks of the single-particle spectral function. arXiv:1806.05216v2 [cond-mat.str-el]

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Section: Methodsmentioning

confidence: 99%

Quantum spin fluctuations and evolution of electronic structure in cuprates

et al. 2018

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“…An effective bosonic action for charge degrees of freedom can be derived following transformations, as presented in a recent work [49]. There, the lattice action (1) is divided into the local impurity problem of the extended dynamical mean-field theory (EDMFT) [51][52][53][54][55] and the remaining nonlocal part.…”

Section: Bosonic Action For Electronic Chargementioning

confidence: 99%

“…The inverse transformation back to the initial "lattice" space after truncation of the interaction of the dual action at the two-particle level results in the following bosonic action for charge variables (for details see Ref. 49 and Appendix A)…”

Section: Bosonic Action For Electronic Chargementioning

confidence: 99%

“…However, to our knowledge, no attempts to extend this theory to the description of charge fluctuations in the correlated regime and to derive the pair interaction of the Ising model directly from the quantum problem have been reported yet. Additional impulse for investigation of this important problem is given by theoretical studies of magnetism in correlated electronic systems [45][46][47][48][49], where an effective classical Heisenberg model for the quantum problem was derived. Since mag-netism is also a collective electronic property, one may expect that charge degrees of freedom can be treated in a similar way.…”

Section: Introductionmentioning

confidence: 99%

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Effective Ising model for correlated systems with charge ordering

et al. 2019

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Collective electronic fluctuations in correlated materials give rise to various important phenomena, such as charge ordering, superconductivity, Mott insulating and magnetic phases, and plasmon and magnon modes. Unfortunately, the description of these correlation effects requires significant effort, since they almost entirely rely on strong local and nonlocal electron-electron interactions. Some collective phenomena, such as magnetism, can be sufficiently described by simple Heisenberg-like models that are formulated in terms of bosonic variables. This fact suggests that other many-body excitations can also be described by simple bosonic models in the spirit of Heisenberg theory. Here we derive an effective bosonic action for charge degrees of freedom for the extended Hubbard model and define a physical regime where the obtained action reduces to a classical Hamiltonian of an effective Ising model. arXiv:1806.04927v3 [cond-mat.str-el]

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“…If this is the case, the the phase fluctuations are effectively decoupled from the Higgs mode and can be considered independently. Otherwise, amplitude fluctuations of the dSC can become stronger and vertex corrections, that we neglect, become significant 47 . Our calculations show a saturation of Φ CDMFT dSC at T ∼ 0.02 for dopings δ 0.1.…”

Section: Superconducting Stiffnessmentioning

confidence: 99%

Josephson lattice model for phase fluctuations of local pairs in copper oxide superconductors

et al. 2019

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We derive an expression for the effective Josephson coupling from the microscopic Hubbard model. It serves as a starting point for the description of phase fluctuations of local Cooper pairs in d x 2 −y 2wave superconductors in the framework of an effective XY model of plaquettes, the Josephson lattice. The expression for the effective interaction is derived by means of the local-force theorem, and it depends on local symmetry-broken correlation functions that we obtain using the cluster dynamical mean-field theory. Moreover, we apply the continuum limit to the Josephson lattice to obtain an expression for the gradient term in the Ginzburg-Landau theory and compare predicted London penetration depths and Kosterlitz-Thouless transition temperatures with experimental data for YBa2Cu3O7−x . arXiv:1810.12986v2 [cond-mat.str-el]

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Effective Heisenberg Model and Exchange Interaction for Strongly Correlated Systems

Cited by 43 publications

References 74 publications

Quantum spin fluctuations and evolution of electronic structure in cuprates

Quantum spin fluctuations and evolution of electronic structure in cuprates

Effective Ising model for correlated systems with charge ordering

Josephson lattice model for phase fluctuations of local pairs in copper oxide superconductors

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