Ferromagnetism and Elementary Excitations in the Hubbard Model

Nikolaev, M. Yu.; Ryzhanova, N.; Vedyaev, A. V.; Zubritskii, S. M.

doi:10.1002/pssb.2221280217

Cited by 17 publications

(3 citation statements)

References 5 publications

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“…However, it should be borne in mind that in this concentration range (almost half-filled band) allowance for the interaction of holes with spin deviations is of crucial importance. This follows from a paper by Nagaoka [6], who has given an exact stability criterion for the ferromagnetic state at K G 1 and (1 -n ) G 1 (for this problem, see also [4]). For the first time, the importance of taking into account the electron-magnon interaction in the Hubbard model has been explicitly indicated in [18].…”

mentioning

confidence: 99%

A diagram technique for Hubbard operators: the magnetic phase diagram in the (t-J) model

Izyumov¹,

Letfulov²

1990

J. Phys.: Condens. Matter

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The authors construct a diagram technique for the (t-J) model Hamiltonian expressed in terms of Hubbard operators. This technique combines features of the diagram technique for normal Fermi systems and those for the Heisenberg model with spin operators. The general graphic structure is identified for one-particle Green functions composed of Hubbard operators. The (t-J) model has logical consistency, is reasonably simple and can serve as a working tool in exploring various properties of this model. To an approximation that resides in summing ladder-type diagrams with antiparallel electron lines, the authors calculate the system's magnetic susceptibility. A formula is derived which reflects the dual nature of the magnetic states in the Hubbard model; this duality manifests itself in the presence of a localised and an itinerant contribution in the bare susceptibility. The authors trace how the relative value of the localised contribution varies as the electron concentration is increased from 0 to 1. With n>2/3, the paramagnetic phase of the system becomes unstable with respect to the occurrence of ferromagnetic or antiferromagnetic ordering. A magnetic phase diagram for zero temperature is constructed on the (t/U, n) plane.

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mentioning

confidence: 99%

A diagram technique for Hubbard operators: the magnetic phase diagram in the (t-J) model

Izyumov¹,

Letfulov²

1990

J. Phys.: Condens. Matter

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“…In the technique [22,23] one more open question exists, namely, as has been shown [24], compared to the conventional DT for fermions and bosons the set of diagrams in the DT for the s-band Hubbard model is not unique, being dependent on the order in which different Xoperators are picked up from the chronologically ordered product ͗T{X 1 ( 1 ) ⅐ ⅐ ⅐ X m () ⅐ ⅐ ⅐ X n ( n )}͘ for Wick's decoupling. To avoid under-or double counting, this way of the formulation of the DT must be complemented by a system of priority, or hierarchy, for the X-operators.…”

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confidence: 99%

“…Third, despite the allowance of mixing interaction between localized and delocalized electrons the atomic-like Hund's rules can be taken into account (already at the level of constructing of the zero Hamiltonian). Fourth, the possible degeneracy of many-electron states involved is taken into account by the form (24), (52), or (53) of the population numbers. Fifth, because the single-site contributions from the Coulomb and exchange interactions are included by construction into the energies of many-electron states E ⌫ the calculation of an effective exchange interaction between the angular momenta (also, interaction between quadrupole momenta, .…”

Section: Hubbard-i Approximationmentioning

confidence: 99%

Theory of strongly correlated electron systems: Hubbard–Anderson models from an exact Hamiltonian, and perturbation theory near the atomic limit within a nonorthogonal basis set

Sandalov

Johansson

Eriksson

2003

Int J of Quantum Chemistry

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ABSTRACT:The theory of correlated electron systems is formulated in a form that allows the use as a reference point a density functional theory in the local density approximation (LDA DFT) for solids or molecules. The theory is constructed in two steps. As a first step, the total Hamiltonian is transformed into a correlated form. To elucidate the microscopic origin of the parameters of the periodic Hubbard-Anderson model (PHAM) the terms of the full Hamiltonian that have the operator structure of PHAM are separated. It is found that the matrix element of mixing interaction includes ion configuration-and number of particles-dependent contributions from the Coulomb interaction. In a second step the diagram technique (DT) is developed by means of generalization of the Baym-Kadanoff method for correlated systems. The advantages of the method are that: (1) A nonorthogonal basis can be used, in particular the one generated by LDA DFT; (2) the equations for Green's functions (GFs) for the Fermi and Bose types of quasiparticles can be formulated in the form of a closed system of functional equations. The latter allows us to avoid the question of the nonunique decoupling procedure existing in previous versions of the DT and perform the expansion in terms of dressed GFs. Although the expressions for all interactions depend on the overlap matrix, it is shown that the theory is formally equivalent to one with orthogonal states with redefined interactions. When the PHAM is treated from the atomic-limit side the vertexes are generated by kinematic interactions. The latter arise due to nontrivial commutation relations between X-operators and come from the mixing, hopping, and overlap of states. The equations for GFs are derived within the nonorthogonal basis set in Hubbard-I, one-loop and random-phase approximations with respect to kinematic interactions. The self-consistent equation for "Hubbard Us" is derived. The technique developed is general, in particular its "bosonic" part can be used for description of spin systems with arbitrary anisotropy, systems with orbital ordering, or ordering of multipoles.

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Many‐electron operator approach in the solid state theory

Irkhin

1994

Physica Status Solidi (b)

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Ferromagnetism and Elementary Excitations in the Hubbard Model

Cited by 17 publications

References 5 publications

A diagram technique for Hubbard operators: the magnetic phase diagram in the (t-J) model

A diagram technique for Hubbard operators: the magnetic phase diagram in the (t-J) model

Theory of strongly correlated electron systems: Hubbard–Anderson models from an exact Hamiltonian, and perturbation theory near the atomic limit within a nonorthogonal basis set

Many‐electron operator approach in the solid state theory

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