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Journal articles on the topic 'Slave bosons'

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Published: 23 November 2024

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1

Ziegler, K. "Strongly Correlated Bosons on a Lattice: A Slave-Boson Approach." Europhysics Letters (EPL) 23, no. 7 (September 1, 1993): 463–67. http://dx.doi.org/10.1209/0295-5075/23/7/001.

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2

Frésard, R., and P. Wölfle. "Unified Slave Boson Representation of Spin and Charge Degrees of Freedom for Strongly Correlated Fermi Systems." International Journal of Modern Physics B 06, no. 05n06 (March 1992): 685–704. http://dx.doi.org/10.1142/s0217979292000414.

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We consider a slave boson representation of lattice electrons in terms of bosons for the empty, singly and doubly occupied site. The approach generalizes an earlier formulation by Kotliar and Ruckenstein. As examples the Hubbard model and the t-J model are considered. The emphasis is on a detailed derivation and discussion of the formal aspects. Simple meanfield solutions are discussed for illustrative purposes.
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3

Nori, Franco, Gergely T. Zimanyi, and Elihu Abrahams. "HARD-CORE SLAVE-BOSON DESCRIPTION OF GENERALIZED FLUX PHASES." International Journal of Modern Physics B 05, no. 01n02 (January 1991): 119–30. http://dx.doi.org/10.1142/s0217979291000080.

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Through a hard-core slave-boson mean-field approach to the t-J model, which describes the dynamics of holes moving in a quantum antiferromagnet, we investigate its generalized flux phases. We first study the motion of an electron gas for arbitrary fillings and fields and establish the linear proportionality between the filling factor and the optimal flux with high accuracy. Using this result, we show that if the hard-core nature of the hole bosons is taken into account, then the slave-boson mean-field approximation for the t-J Hamiltonian allows for a solution where both the spinons and the holons experience an average flux of one flux quantum per particle. This enables them to achieve the lowest possible energy within the manifold of spatially-uniform flux states. In the case of the continuum model, this is possible only for certain fractional fillings and we suggest that the system may react to this frustration effect by phase separation.
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4

Kulić, Miodrag L., and Roland Zeyher. "Novel 1/N Expansion for Self-Energy and Correlation Functions of the Hubbard Model." Modern Physics Letters B 11, no. 08 (April 10, 1997): 333–38. http://dx.doi.org/10.1142/s0217984997000414.

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The novel slave-free (i.e. without slave bosons and fermions) approach to the problem of strong correlations is used in studying the Hubbard (t-J) model, where the self-energy is expressed in terms of charge and spin vertex functions of Hubbard operators. A systematic 1/N expansion (N is the number of spin components) of the self-energy is carried out. In O(1) it gives the same quasiparticle spectrum as the slave boson theory. The next order O(1/N) of the self-energy Σ(k, ω) is calculated exactly by solving analytically the integral equations for the charge and spin vertices. As an example for the feasibility of the proposed method explicit results for Σ(k, ω) are given in the case J=0. Dealing only with observable quantities our method is transparent and easily applicable to models which exclude double occupancy on lattice sites, such as the Anderson model and the Emery model for high temperature superconductors.
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5

Fröhlich, J., and P. A. Marchetti. "Slave fermions, slave bosons, and semions from bosonization of the two-dimensionalt-Jmodel." Physical Review B 46, no. 10 (September 1, 1992): 6535–52. http://dx.doi.org/10.1103/physrevb.46.6535.

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6

Krawiec, Mariusz, and Karol I. Wysokiński. "Superconductivity in correlated systems: Constraint quantization of slave bosons." Physical Review B 59, no. 14 (April 1, 1999): 9500–9507. http://dx.doi.org/10.1103/physrevb.59.9500.

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7

TUAN, HOANG ANH, NGUYEN TOAN THANG, and NGUYEN NGOC THUAN. "SUPERCONDUCTING IN THE NEAR HALF-FILLING HUBBARD MODEL." Modern Physics Letters B 09, no. 11n12 (May 20, 1995): 711–17. http://dx.doi.org/10.1142/s0217984995000656.

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The Hubbard model of strongly correlated electron systems is considered near half-filling within the framework of a new functional integral method without slave bosons. A dynamical system of equations determining the superconducting phase of the Hubbard model is derived. Both singlet and triplet Cooper pairings are studied.
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8

Ruckenstein, Andrei E., and Stefan Schmitt-Rink. "New approach to strongly correlated systems:1Nexpansions without slave bosons." Physical Review B 38, no. 10 (October 1, 1988): 7188–91. http://dx.doi.org/10.1103/physrevb.38.7188.

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9

WOJCIECHOWSKI, R., and L. KOWALEWSKI. "ON THE MAGNETOACOUSTIC OSCILLATIONS IN HEAVY FERMION COMPOUNDS." International Journal of Modern Physics B 07, no. 01n03 (January 1993): 67–70. http://dx.doi.org/10.1142/s0217979293000172.

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Using the Green's function technique and MFA for the slave bosons approach, we consider the influence of the magnetic field on the oscillations of the sound velocity in cerium-based heavy fermion compounds. The quasiparticle-phonon interaction is assumed to result from the volume dependence of the spin fluctuation temperature T *. We obtain magnetic oscillations of the sound velocity at finite temperature. The mass enhancement and the renormalised Fermi energy are the same as those obtained for the magnetic de Haas-van Alphen effect.
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10

Citro, Roberta, and Francesco Romeo. "Non-equilibrium slave bosons approach to quantum pumping in interacting quantum dots." Journal of Physics: Conference Series 696 (March 2016): 012014. http://dx.doi.org/10.1088/1742-6596/696/1/012014.

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11

Denteneer, P. J. H. "Strong-coupling expansion for the Hubbard model in arbitrary dimension using slave bosons." Physical Review B 53, no. 15 (April 15, 1996): 9764–69. http://dx.doi.org/10.1103/physrevb.53.9764.

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12

Frésard, Raymond, Henni Ouerdane, and Thilo Kopp. "Slave bosons in radial gauge: A bridge between path integral and Hamiltonian language." Nuclear Physics B 785, no. 3 (December 2007): 286–306. http://dx.doi.org/10.1016/j.nuclphysb.2007.05.025.

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13

RISEBOROUGH, PETER S. "MAGNETIC PROPERTIES OF HEAVY FERMION SEMI-CONDUCTORS." International Journal of Modern Physics B 07, no. 01n03 (January 1993): 58–61. http://dx.doi.org/10.1142/s0217979293000159.

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The heavy fermion semi-conductors, such as Ce 3 Bi 4 Pt 3 or CeNiSn, are modeled by the Anderson Lattice Hamiltonian. In the limit of large coulomb interaction, the strong electron-electron correlations can be re-expressed in terms of slave bosons. The resulting model is treated in the mean field approximation. In this approximation, the model exhibits a transition between a low temperature semi-conducting state and a high temperature state. The high temperature state may be characterized as having an uncorrelated metallic conduction band and a set of independent local moments, whereas the low temperature state can be described as a highly correlated indirect gap semi-conductor. The dynamic magnetic response function is calculated, for the low temperature phase.
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14

Nakano, Yuki, Takumi Ishima, Naohiro Kobayashi, Kazuhiko Sakakibara, Ikuo Ichinose, and Tetsuo Matsui. "Thet-Jmodel of hard-core bosons in slave-particle representation and its Monte-Carlo simulations." Journal of Physics: Conference Series 400, no. 3 (December 17, 2012): 032064. http://dx.doi.org/10.1088/1742-6596/400/3/032064.

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15

Frésard, Raymond, and Thilo Kopp. "Slave bosons in radial gauge: the correct functional integral representation and inclusion of non-local interactions." Nuclear Physics B 594, no. 3 (February 2001): 769–89. http://dx.doi.org/10.1016/s0550-3213(00)00657-x.

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16

BOIES, DANIEL, F. A. JACKSON, and A. M. S. TREMBLAY. "NAGAOKA FERROMAGNETISM AS A TEST OF SLAVE-FERMION AND SLAVE-BOSON APPROACHES." International Journal of Modern Physics B 09, no. 09 (April 20, 1995): 1001–24. http://dx.doi.org/10.1142/s0217979295000409.

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The ferromagnetic to paramagnetic transition in the Nagaoka (U=∞) limit of the Hubbard Hamiltonian is used to test the applicability of slave-boson and slave-fermion (Schwinger boson) functional-integral approaches. Within the slave-fermion formalism to one-loop order, the ferromagnetic phase is stable to spin-wave, gauge field, and longitudinal fluctuations over a doping interval that is much too large compared with other approaches. Furthermore, nonbipartite lattices such as hcp or fcc lattices are ferromagnetic for t>0 over a wider doping interval than for t<0, in qualitative disagreement with all other types of calculations. It is possible to remedy all these defects in order to reach agreement, at least qualitatively, with previous studies. It suffices to take the point of view that in the U=∞ limit it is best to represent the paramagnetic phase as the mean-field solution of the slave-boson representation, and the ferromagnetic phase as the mean-field solution of the slave-fermion representation. The transition between both phases is taken to occur at the critical hole doping where the ground state energies are equal. This seems to give the best possible comparison with other approaches, despite the lack of a variational principle justifying comparisons of energies between slave-fermion and slave-boson representations. On bipartite lattices, the critical hole density found analytically by this procedure, δc=1/3, is identical to the critical density obtained in the Kotliar-Ruckenstein slave-boson approach. This value of δc is also close to various other estimates. Nevertheless, non-bipartite lattices with t>0 remain ferromagnetic over a small but finite doping interval, in quantitative disagreement with some other approaches.
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17

DUC, HUYNH THANH, and NGUYEN TOAN THANG. "MAGNETIC IMPURITY IN A SYSTEM OF INTERACTING ELECTRONS." Modern Physics Letters B 13, no. 24 (October 20, 1999): 849–58. http://dx.doi.org/10.1142/s0217984999001044.

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The Kondo effect of the Anderson impurity in a correlated conduction electron system is studied with the slave boson mean-field theory. The interacting conduction electrons are described by a Hubbard model with an interaction of strength U. It is shown that the Kondo temperature T K decreases with an increase of U. In the intermediate regime at half-filling, the exponential scale of the Kondo temperature T K is already lost at the saddle-point level of slave boson formulation.
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18

Dzhunushaliev, Vladimir. "Non-associative slave-boson decomposition." Journal of Generalized Lie Theory and Applications 1, no. 2 (2007): 129–34. http://dx.doi.org/10.4303/jglta/s070205.

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19

Hualde, J. M. Aguiar, G. Chiappe, and E. V. Anda. "Kondo spin splitting with slave boson." Brazilian Journal of Physics 36, no. 3b (September 2006): 917–21. http://dx.doi.org/10.1590/s0103-97332006000600032.

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20

Lilly, Leonhard, Alejandro Muramatsu, and Werner Hanke. "Slave-boson results for experimental observables." Physica C: Superconductivity 185-189 (December 1991): 1615–16. http://dx.doi.org/10.1016/0921-4534(91)90934-q.

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21

VAN HIEU, NGUYEN, HA VINH TAN, and NGUYEN TOAN THANG. "DERIVATION OF EQUATIONS FOR HIGH Tc BY MEANS OF SLAVE BOSON TECHNIQUE." International Journal of Modern Physics B 03, no. 01 (January 1989): 103–7. http://dx.doi.org/10.1142/s0217979289000099.

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The "slave boson" technique is applied for studying the superconductivity of the system of strongly correlated electrons with the Hubbard Hamiltonian. On the basis of the Green functions equations for the new boson and fermion operators we derive the dynamical equations determining the order parameters of the given RVB model.
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22

ISODA, M. "ON THE THERMODYNAMICAL PROPERTIES IN THE SLAVE BOSON MEAN FIELD THEORY OF HUBBARD MODEL." International Journal of Modern Physics B 07, no. 01n03 (January 1993): 597–600. http://dx.doi.org/10.1142/s0217979293001256.

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The effect of spin polarization in the slave boson mean field theory in the strongly correlated Heavy electron systems is discussed concerning the thermodynamical properties of the Hubbard model. The free energy is evaluated by taking into account the effective reduction of the quantum states due to the exclusion of double occupation in a site through the introduction of the spin-dependent slave boson. The magnetic susceptibility, calculated as a function of temperature, shows the Fermi liquid property at low temperature and the local moment behaviour with the proper Curie constant at high temperature. The present results, including the temperature dependence of the specific heat, are compared with the previous results without the reduction of quantum states.
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23

CAPRARA, SERGIO, MASSIMO CAPONE, LUCA CAPRIOTTI, and FEDERICO BECCA. "COMMENSURATE VERSUS INCOMMENSURATE SPIN-ORDERING IN THE TRIANGULAR HUBBARD MODEL." International Journal of Modern Physics B 14, no. 29n31 (December 20, 2000): 3386–91. http://dx.doi.org/10.1142/s0217979200003708.

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The presence of incommensurate spin structures in the half-filled triangular Hubbard model, where frustration leads to a competition among different magnetic phases, is investigated using both the slave-boson technique, and exact diagonalization of finite clusters. We also investigate the metal-insulator transition which, due to the lack of perfect nesting, takes place at a finite value of U. Within the slave-boson approach, as the interaction grows the paramagnetic metal turns into a metallic phase with incommensurate spiral ordering. Increasing further the interaction, a linear spin-density-wave is stabilized, and finally for strong coupling the latter phase undergoes a first-order transition towards an antiferromagnetic insulator. No trace of the intermediate phases is instead found in the exact diagonalization results.
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24

ZANDRON, O. S. "THE HUBBARD OPERATORS AND THE SLAVE-PARTICLES PATH-INTEGRAL REPRESENTATIONS DESCRIBING THE t-J MODEL." International Journal of Modern Physics B 21, no. 11 (April 30, 2007): 1861–74. http://dx.doi.org/10.1142/s0217979207037077.

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In the present work it is shown that the family of first-order Lagrangians for the t-J model and the corresponding correlation generating functional previously found can be exactly mapped into the slave-fermion decoupled representation. Next, by means of the Faddeev-Jackiw symplectic method, a different family of Lagrangians is constructed and it is shown how the corresponding correlation generating functional can be mapped into the slave-boson decoupled representation.
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25

W�lfle, Peter. "Slave boson theories of correlated electron systems." Journal of Low Temperature Physics 99, no. 3-4 (May 1995): 625–35. http://dx.doi.org/10.1007/bf00752353.

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26

Arrigoni, E., G. Strinati, and C. Castellani. "Antiferromagnetism ofCuO2layers within a slave-boson approach." Physical Review B 41, no. 7 (March 1, 1990): 4838–41. http://dx.doi.org/10.1103/physrevb.41.4838.

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27

Le, Duc-Anh. "Mott transition in the dynamic Hubbard model within slave boson mean-field approach." Modern Physics Letters B 28, no. 10 (April 20, 2014): 1450078. http://dx.doi.org/10.1142/s021798491450078x.

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At zero temperature, the Kotliar–Ruckenstein slave boson mean-field approach is applied to the dynamic Hubbard model. In this paper, the influences of the dynamics of the auxiliary boson field on the Mott transition are investigated. At finite boson frequency, the Mott-type features of the Hubbard model is found to be enhanced by increasing the pseudospin coupling parameter g. For sufficiently large pseudospin coupling g, the Mott transition occurs even for modest values of the bare Hubbard interaction U. The lack of electron–hole symmetry is highlighted through the quasiparticle weight. Our results are in good agreement with the ones obtained by two-site dynamical mean-field theory and determinant quantum Monte Carlo simulation.
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28

Gilmutdinov V. F., Timirgazin M. A., and Arzhnikov A. K. "Spiral magnetic order and metal-insulator transition in the Hubbard model on a triangular lattice." Physics of the Solid State 64, no. 1 (2022): 76. http://dx.doi.org/10.21883/pss.2022.01.52492.191.

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The magnetic phase diagrams of the two-dimensional Hubbard model forisotropic and anisotropic triangular lattices are constructed within theHartree--Fock and slave boson approximations. The triangular latticespecific non-collinear and spiral magnetic states, as well as phaseseparation between them, are shown to be realized in a wide range of modelparameters along with collinear magnetic states (stripe antiferromagneticand ferromagnetic). Phase transitions of the first and second order arefound, and the boundaries of the phase separation regions are determined. A comparison of the two approximations, Hartree--Fock and slave boson, showsthat electronic correlations suppress magnetic states, the region ofparamagnetism being expand, for values U/t>~=5. At the same time, when theFermi level is near the van Hove singularity, electron correlations do notchange the diagrams qualitatively, which is consistent with the previouslyobtained result for square and cubic lattices. The results are comparedwith the data available in the literature for other methods and approaches. Keywords: Hubbard model, phase separation, spiral magnetic order, triangular lattice, metal-insulator transition\
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29

Гильмутдинов, В. Ф., М. А. Тимиргазин, and А. К. Аржников. "Спиральное магнитное упорядочение и переход металл--диэлектрик в модели Хаббарда на треугольной решeтке." Физика твердого тела 64, no. 1 (2022): 79. http://dx.doi.org/10.21883/ftt.2022.01.51835.191.

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The magnetic phase diagrams of the two-dimensional Hubbard model for isotropic and anisotropic triangular lattices are constructed within the Hartree-Fock and slave boson approximations. The triangular lattice specific non-collinear and spiral magnetic states, as well as phase separation between them, are shown to be realized in a wide range of model parameters along with collinear magnetic states (stripe antiferromagnetic and ferromagnetic). Phase transitions of the first and second order are found, and the boundaries of the phase separation regions are determined. A comparison of the two approximations, Hartree-Fock and slave boson, shows that electronic correlations suppress magnetic states, the region of paramagnetism being expand, for values U/t>5. At the same time, when the Fermi level is near the van Hove singularity, electron correlations do not change the diagrams qualitatively, which is consistent with the previously obtained result for square and cubic lattices. The results are compared with the data available in the literature for other methods and approaches.
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30

LEE, SUNG-SIK, and SUNG-HO SUCK SALK. "HOLON-PAIR CONDENSATION OF HIGH Tc CUPRATES: SUPERSYMMETRY CONDITIONS." International Journal of Modern Physics B 13, no. 29n31 (December 20, 1999): 3455–59. http://dx.doi.org/10.1142/s0217979299003209.

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Based on the t–J Hamiltonian of U(1) slave-boson symmetry it is shown from our derived free energy that symmetry breaking can occur to allow holon-pair bose condensation. Supersymmetry conditions are proposed based on our derived quasiparticle Hamiltonian involving both spinons and holons.
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31

Biagini, M. "Electronic Structure Calculations forYBa2Cu3O7within the Slave Boson Formalism." Physical Review Letters 77, no. 19 (November 4, 1996): 4066–69. http://dx.doi.org/10.1103/physrevlett.77.4066.

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32

Brinckmann, Jan, and Patrick A. Lee. "Slave Boson Approach to Neutron Scattering inYBa2Cu3O6+ySuperconductors." Physical Review Letters 82, no. 14 (April 5, 1999): 2915–18. http://dx.doi.org/10.1103/physrevlett.82.2915.

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33

Kim, Y. B., and Z. Wang. "Quantum-disordered slave-boson theory of underdoped cuprates." Europhysics Letters (EPL) 50, no. 5 (June 1, 2000): 656–62. http://dx.doi.org/10.1209/epl/i2000-00320-5.

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34

LEE, H. C. "ONE-ELECTRON SPECTRAL WEIGHT OF DOPED MOTT INSULATORS IN GAUGE FIELD THEORY APPROACH." International Journal of Modern Physics B 10, no. 27 (December 15, 1996): 3727–36. http://dx.doi.org/10.1142/s0217979296002038.

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The electron spectral weight of doped Mott insulators based on the two-dimensional slave boson gauge field theory is studied. The vertex correction with static gauge field is calculated in the second order perturbation theory. The vertex correction is found to be singular at low energy and requires non-perturbative treatments.
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35

Irkhin, Valentin Yu. "Ideas by S.V. Vonsovsky and Modern Model Treatment of Magnetism." Solid State Phenomena 168-169 (December 2010): 3–11. http://dx.doi.org/10.4028/www.scientific.net/ssp.168-169.3.

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A review of fundamental works by Shubin and Vonsovsky on the formulation of the polar and s–d(f) exchange models is given. Their ideas are compared with subsequent developments in the theory of magnetism in d- and f-metals and their compounds. Modern approaches including various slave-boson and slave-fermion representations, formation of exotic quasiparticles etc. are discussed. Internal connections between different many-electron models (the Heisenberg, Hubbard, t–J, Anderson Hamiltonians) are presented. Description of anomalous rare-earth and actinide compounds (Kondo lattices, systems with heavy fermions and non-Fermi-liquid behavior) within the framework of the s–d(f) exchange model and related models is considered.
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36

Castellani, C., C. Di Castro, and M. Grilli. "KONDO LATTICE HAMILTONIAN FOR HIGH Tc SUPERCONDUCTORS." International Journal of Modern Physics B 02, no. 05 (October 1988): 659–65. http://dx.doi.org/10.1142/s0217979288000482.

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In the framework of a slave boson approach we show that the inclusion of a narrow metallic band inside the bonding-antibonding [Formula: see text] gap results in an effective Kondo lattice Hamiltonian which may be relevant for the description of the high Tc superconductors. Depending on the relative values of the effective parameters different scenarios follow.
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37

Zhang, L., J. K. Jain, and V. J. Emery. "Importance of the local constraint in slave-boson theories." Physical Review B 47, no. 6 (February 1, 1993): 3368–73. http://dx.doi.org/10.1103/physrevb.47.3368.

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38

Raimondi, R., and C. Castellani. "Lower and upper Hubbard bands: A slave-boson treatment." Physical Review B 48, no. 15 (October 15, 1993): 11453–56. http://dx.doi.org/10.1103/physrevb.48.11453.

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39

Schwab, P., and R. Raimondi. "Andreev tunneling in quantum dots: A slave-boson approach." Physical Review B 59, no. 3 (January 15, 1999): 1637–40. http://dx.doi.org/10.1103/physrevb.59.1637.

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40

Goswami, Partha. "Investigation of extended Hubbard model by slave-boson method." Physica B: Condensed Matter 403, no. 5-9 (April 2008): 999–1001. http://dx.doi.org/10.1016/j.physb.2007.10.076.

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41

Franco, R., M. S. Figueira, and M. E. Foglio. "X-slave boson approach to the periodic Anderson model." Journal of Magnetism and Magnetic Materials 226-230 (May 2001): 194–95. http://dx.doi.org/10.1016/s0304-8853(00)01120-3.

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42

Seibold, G., and E. Sigmund. "Gutzwiller and slave-boson methods for intersite Coulomb interactions." Zeitschrift für Physik B Condensed Matter 101, no. 3 (December 1997): 405–10. http://dx.doi.org/10.1007/s002570050226.

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43

Bang, Yunkyu, and G. Kotliar. "Optical conductivity in thet-Jmodel: Slave-boson, large-Ntechnique." Physical Review B 48, no. 13 (October 1, 1993): 9898–901. http://dx.doi.org/10.1103/physrevb.48.9898.

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44

Karbowski, Jan. "Quantum fluctuations in the Kondo insulators: Slave-boson approach." Physical Review B 54, no. 2 (July 1, 1996): R728—R731. http://dx.doi.org/10.1103/physrevb.54.r728.

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45

Frésard, R., and T. Kopp. "Exact results with the Kotliar-Ruckenstein slave-boson representation." Annalen der Physik 524, no. 3-4 (January 26, 2012): 175–81. http://dx.doi.org/10.1002/andp.201100197.

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46

CAPRARA, S. "CHARGE AND SPIN MODULATION IN THE PRESENCE OF A DIMERIZED CRYSTAL FIELD." International Journal of Modern Physics B 14, no. 29n31 (December 20, 2000): 3392–97. http://dx.doi.org/10.1142/s0217979200003861.

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I study the evolution of the antiferromagnetic ground state of the half-filled Hubbard model in the presence of a charge modulation induced by the dimerization of the crystal field, making use of the slave-boson approach. I also discuss how the model can be extended to describe the neutral-to-ionic transition which occurs in some organic mixed-stack donor-acceptor crystals.
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47

Wölfle, P. "SPIN-CARRYING SLAVE BOSON REPRESENTATION FOR STRONGLY CORRELATED FERMION SYSTEMS." International Journal of Modern Physics B 03, no. 12 (December 1989): 1833–42. http://dx.doi.org/10.1142/s0217979289001172.

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We consider slave boson formulations of the Hubbard model, the t–J model and the Anderson model, in which spin and charge fermion degrees of freedom are represented by Bose fields. The approach has been applied to the Hubbard model generalizing the formulation of Kotliar and Ruckenstein. There the Gutzwiller solution is recovered as a saddle point. The method allows to find other types of mean field solutions in a systematic way. Dynamical correlation functions in mean field approximation as well as fluctuation contributions are also calculated.
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48

Jolicoeur, Th, and J. C. Le Guillou. "Fluctuations beyond the Gutzwiller approximation in the slave-boson approach." Physical Review B 44, no. 5 (August 1, 1991): 2403–6. http://dx.doi.org/10.1103/physrevb.44.2403.

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49

Sofo, J. O., and C. A. Balseiro. "Slave-boson mean-field theory for the negative-UHubbard model." Physical Review B 45, no. 1 (January 1, 1992): 377–82. http://dx.doi.org/10.1103/physrevb.45.377.

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50

Li, T., P. Wölfle, and P. J. Hirschfeld. "Spin-rotation-invariant slave-boson approach to the Hubbard model." Physical Review B 40, no. 10 (October 1, 1989): 6817–21. http://dx.doi.org/10.1103/physrevb.40.6817.

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