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Superconductivity and Charge-Density Wave Phase in the Holstein Model: a Weak Coupling Limit

100%
Grzybowski P., Micnas R.
Acta Physica Polonica A
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2007
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vol. 111
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issue 4
453-463
EN
The variational canonical transformation method has been applied to the Holstein model to obtain an effective polaronic Hamiltonian, which is subsequently analyzed in the limit of a weak effective electron-electron interaction. A competition between the superconducting and charge-density wave phases has been studied in the light of strong polaronic effects. The phase diagrams illustrating the system evolution from adiabatic to anti-adiabatic limit are presented.
2
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Towards Spin-Wave Like Approach to the J-J' Heisenberg Antiferromagnet in Terms of Composite Spins

100%
Grzybowski P., Chhajlany R.
Acta Physica Polonica A
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2009
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vol. 115
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issue 1
168-170
EN
Conventional spin-wave approach relies on an expansion around a relevant classical (unentangled) ground state or equivalently the ground state in the mean field approximation for the quantum model. However, for systems which may admit valence bond ground states, such as the staggered J-J' Heisenberg antiferromagnet, single site mean field approximation is obviously an incorrect zeroth order approximation. In this paper, we introduce a mean field approximation for clusters consisting of two spins connected by a strong bond in the aforementioned model. We identify the quantum critical point and calculate the ground state magnetization within this cluster mean field approximation in one and two dimensions. Finally, we derive an effective dimer Hamiltonian, in the standard basis operator formalism, which may be a basis for further spin-wave like expansions around the cluster mean field approximation ground state.
3
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Effects of Frustrating Hopping on Charge Ordered States in Itinerant Fermion Systems for Arbitrary Concentration in 2D Lattice

81%
Czart W., Grzybowski P., Nogala M., Robaszkiewicz S.
Acta Physica Polonica A
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2012
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vol. 121
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issue 4
828-831
EN
There is ongoing, intense, research in the field of electron charge orderings (CO) and charge density waves phenomena, due to experimental discovery of such phases in numerous important compounds. The aim of this work is to extend recent advances in the field by studying two simple effective paradigmatic models used to describe CO in narrow band materials i.e. (i) a model of correlated electrons: the so-called t-W model of spinless fermions with repulsive interaction W and (ii) the molecular crystal model with the coupling of electrons to intramolecular (crystal field) vibrations in the static limit. The finite temperature phase diagrams are evaluated at arbitrary carriers concentration for several representative cases. Our calculations are performed within the (broken symmetry) HFA for d=2 square lattice and arbitrary carriers concentration. In this contribution we focus on the effects of next-nearest-neighbor hopping on the CO states in these systems and the problem of phase separations involving checkerboard CO with the nesting vector Q=(π,π). The results we show here are an extension of our previous work on the subject.
4
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Charge Orderings and Phase Separations in Itinerant Fermion Systems at Half Filling

81%
Czart W., Grzybowski P., Nogala M., Robaszkiewicz S.
Acta Physica Polonica A
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2012
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vol. 121
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issue 5-6
1042-1044
EN
We analyse the ground state phase diagrams of the charge orderings in narrow band materials using two effective models: (1) the spinless fermion model (t - W) with repulsive intersite interaction (W_{ij} > 0) and (2) the molecular crystal model with the coupling of electrons to intramolecular (crystal field) vibrations. We present results for the case of half filled bands for d = 2 square lattice. The calculations are performed within the (broken symmetry) Hartree-Fock approximation. The study takes into consideration the effects of frustrating next-nearest-neighbour hopping (t_2) on the charge ordered states in these systems. We focus on the two cases: (i) homogeneous phases and phase separations involving checkerboard charge ordering with the nesting vector Q= (π,π) only and (ii) homogeneous phases and phase separations involving two types of charge ordering: (a) checkerboard charge ordering with the nesting vector Q = (π,π), and (b) collinear (CL) charge ordering with Q = (0,π) or Q = (π,0).
5
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Charge Ordering and Phase Separations in the Molecular Crystal Model

81%
Czart W., Grzybowski P., Robaszkiewicz S.
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issue 2
369-372
EN
We analyse the ground state phase diagrams and thermodynamic properties of charge orderings in narrow band materials using the molecular crystal model in the static limit. We present results for the hypercubic lattices in dimensions d = 2 and d = ∞. We focus our study on the problem of phase separations involving charge orderings and the effects of next-nearest-neighbor hopping (t_2) on the charge ordered states in these systems. The ground state phase diagrams are evaluated for a few representative cases. Results for the molecular crystal model are compared with those obtained previously for the spinless fermion model with repulsive intersite interaction W.
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