The recently proposed diagrammatic expansion (DE) technique for the full Gutzwiller wave function (GWF) is applied to the Anderson lattice model (ALM). This approach allows for a systematic evaluation of the expectation values with GWF in the finite
dimensional systems. It introduces results extending in an essential manner those obtained by means of standard Gutzwiller Approximation (GA) scheme which is variationally exact only in infinite dimensions. Within the DE-GWF approach we discuss principal paramagnetic properties of ALM and their relevance to heavy fermion systems. We demonstrate the formation of an effective, narrow $f$-band originating from atomic $f$-electron states and subsequently interpret this behavior as a mutual intersite $f$-electron coherence; a combined effect of both the hybridization and the Coulomb repulsion. Such feature is absent on the level of GA which is equivalent to the zeroth order of our expansion. Formation of the hybridization- and electron-concentration-dependent narrow effective $f$-band rationalizes common assumption of such dispersion of $f$ levels in the phenomenological modeling of the band structure of CeCoIn$_5$. Moreover, we show that the emerging $f$-electron coherence leads in a natural manner to three physically distinct regimes within a single model, that are frequently discussed for 4$f$- or 5$f$- electron compounds as separate model situations. We identify these regimes as: (i) mixed-valence regime, (ii) Kondo-insulator border regime, and (iii) Kondo-lattice limit when the $f$-electron occupancy is very close to the $f$ electrons half-filling, $langlehat n_{f}ranglerightarrow1$. The non-Landau features of emerging correlated quantum liquid state are stressed.
We discuss the Hubbard model in an applied magnetic field and analyze the properties of neutral spin-1/2 fermions within the so-called statistically consistent Gutzwiller approximation (SGA). The magnetization curve reproduces in a semiquantitative m
anner the experimental data for liquid 3 He in the regime of moderate correlations and in the presence of small number of vacant cells, modeled by a non-half filled-band situation, when a small number of vacancies (up to 5%) is introduced in the virtual fcc lattice. We also present the results for the magnetic susceptibility and the specific heat, in which a metamagnetic-like behavior is also singled out in a non-half-filled band case.
We discuss a simple phenomenological Landau theory of phase transitions with two coupled single-component order parameters and compare the results with available experimental data. The model corresponds to the case of a ferroic system, in which ferro
magnetic and ferroelectric transitions originally occur at temperatures $T_M$ and $T_f$, respectively. For $T_f>T_M$ the magnetoelectric coupling strongly renormalizes the magnetic transition temperature, $T_Mto T_{RM}$ (with $T_{RM}>>T_M$), as well as generates an additional anomaly in ferroelectric subsystem $T_{RM}$. Full susceptibility tensor has also been determined. The concept of textit{Arrot plot} is replaced by the textit{Arrot planes} which appear when both types of order coexist. The results are in good overall agreement with experimental data for the ferroelectromagnetic BiMnO$_3$. We also estimate the contribution of Gaussian fluctuations of both order parameters, that lead to corrections to the mean-field specific heat. Those corrections are still insufficient even though other quantities agree quite well with experiment. We calculate the temperature dependence of the coherence length for both types of order as well.
We formulate a complete microscopic theory of a coupled pair of bound magnetic polarons, the bound-magnetic-polaron molecule (BMPM) in a diluted magnetic semiconductor (DMS) by taking into account both a proper two-body nature of the impurity-electro
n wave function and within the general spin-rotation-invariant approach to the electronic states. We also take into account both the Heisenberg and the antiferromagnetic kinetic-exchange interactions, as well as the ferromagnetic coupling within the common spin BMPM cloud. The thermodynamic fluctuations of the spin cloud within the polaron effective Bohr radius of each polaron are taken as Gaussian.
We discuss a detailed phase diagram and other microscopic characteristics on the applied magnetic field - temperature (H_a-T) plane for a simple model of correlated fluid represented by a two-dimensional (2D) gas of heavy quasiparticles with masses d
ependent on the spin direction and the effective field generated by the electron correlations. The consecutive transitions between the Bardeen-Cooper-Schrieffer (BCS) and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases are either continuous or discontinuous, depending on the values of H_a and T. In the latter case, weak metamagnetic transitions occur at the BCS-FFLO boundary. We single out two different FFLO phases, as well as a reentrant behaviour of one of them at high fields. The results are compared with those for ordinary Landau quasiparticles in order to demonstrate the robustness of the FFLO states against the BCS state for the case with spin-dependent masses (SDM). We believe that the mechanism of FFLO stabilization by SDM is generic: other high-field low-temperature (HFLT) superconducting phases benefit from SDM as well.
Paired state of nonstandard quasiparticles is analyzed in detail in two model situations. Namely, we consider the Cooper-pair bound state and the condensed phase of an almost localized Fermi liquid (ALFL) composed of quasiparticles in a narrow-band w
ith the spin-dependent masses (SDM) and an effective field, both introduced earlier and induced by strong electronic correlations. Each of these novel characteristics are calculated in a self-consistent manner. We analyze the bound states as a function of Cooper-pair momentum q in applied magnetic field in the strongly Pauli limiting case (i.e. when the orbital effects of applied magnetic field are disregarded). The spin-direction dependence of the effective mass makes the quasiparticles comprising Cooper pair spin distinguishable in the quantum mechanical sense, whereas the condensed gas of pairs may still be regarded as composed of identical entities. The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) condensed phase of moving pairs is by far more robust in the applied field for the case with spin-dependent masses than in the situation with equal masses of quasiparticles. Relative stability of the Bardeen-Cooper-Schrieffer (BCS) vs. FFLO phase is analyzed in detail on temperature - applied field plane. Although our calculations are carried out for a model situation, we can conclude that the spin-dependent masses should play an important role in stabilizing high-field low-temperature (HFLT) unconventional superconducting phases (FFLO being an instance) in systems such as CeCoIn_5, organic metals, and possibly others.
In this overview I sketch briefly the path to the so-called {em t-J model} derived for the first time 30 years ago and provide its original meaning within the theory of strongly correlated magnetic metals with a non-Fermi (non-Landau) liquid ground s
tate. An emergence of the concept of {em real space pairing}, is discussed in a historical prospective. A generalization of this model to the many-orbital situation is briefly discussed. The emphasis is put on didactical exposition of ideas, as they were transformed into mathematical language. The concept of {em hybrid pairing} is introduced in the same context at the end.
