The metallic phase of strongly correlated electrons is discussed within a novel statistical approach that correctly reproduces the principal features of the Mott insulating state when localization is reached at half-filled band (n=1). The entropy in the normal phase decomposes into a spinless-fermion part representing holes, and a part describing localized moments. The explicit form of the gap ${\ensuremath{\Delta}}_{\mathrm{k}}$ is derived; this solution is shown to disappear when n=1. Most of the results cannot be obtained by using the Fermi-Dirac distribution for single-particle states.
The metallic phase of strongly correlated electrons is discussed within a novel statistical approach that correctly reproduces the principal features of the Mott insulating state when localization is reached at half-filled band (n=1). The entropy in the normal phase decomposes into a spinless-fermion part representing holes, and a part describing localized moments. The explicit form of the gap \ensuremathΔk is derived; this solution is shown to disappear when n=1. Most of the results cannot be obtained by using the Fermi-Dirac distribution for single-particle states.
We propose a novel statistical-mechanical approach to a system of strongly correlated electrons in a partially filled narrow band which reproduces rigorously the situation in the atomic limit. In this approach the doubly occupied configurations are excluded both in the real and in the reciprocal spaces. Employing this principle we calculate the thermodynamic properties of those electrons. The metallic state, corresponding to a partially-filled-band case, exhibits a Fermi-liquid--type behavior at low temperatures and transforms into a spin liquid at high temperatures. This feature of our results is reminiscent of the behavior in both magnetic metals and heavy-fermion systems. Additionally, the approach reproduces correctly the statistical properties of the system of localized moments in the limit of the half-filled band, corresponding to the Mott insulating phase. These results are not obtained if one starts from the Fermi-Dirac distribution for the quasiparticles. The last assertion is reinforced by an explicit derivation of a statistical distribution function for correlated electrons which reduces to the Fermi-Dirac distribution in the limit of weak interactions, as well as to the distribution for the spin liquid derived earlier in the limit of strong correlation between the particles.
We summarize recent theoretical results of our group concerning the electronic states of the strongly correlated fermions at nonzero temperature. The state of almost localized fermions is discussed within a mean-field approach for auxiliary bosons, both in the narrow-band (Section 2) and in the hybridized band (Section 3) cases. This state represents a metallic state of correlated fermion systems (such as V{sub 2}O{sub 3}) below the Mott-Hubbard localization threshold. The Fermi liquid state does not describe properly the properties of narrow band electrons in the large Hubbard -- U limit beyond the localization threshold. Therefore, in Section 4 and 5 we introduce a phenomenological concept of statistical spin liquid which describes principal features of a crossover from a high-temperature superconductor to the Mott insulator for a two-dimensional system. It also reproduces the main features of the phase diagram for La{sub 2-x}Sr{sub x}CuO{sub 4} system, which is modelled by a planar structure.
We discuss two different cases of strongly correlated fermions statistics. The first of them is the non-Fermi liquid (NFL) case, i.e. , that of fermions with exclusion of doubly occupancy of quasimomentum states \(\{\mb k\}\) with opposite spins (↑↓). The second is the statistical spin liquid (SSL) case, in which the fermion spins hop around and mix with the holes (unoccupied) states. For both cases, we calculate the system entropy and the corresponding statistical distribution function, analyzed for a two-dimensional square-lattice filling n∈[0,1] and relative temperature kBT/∣t∣, where t<0 is the nearest neighbor hopping integral. We are particularly interested in the situation when the system of itinerant fermions reduce to the Mott-insulator state for the half-filled band (n→1). This limiting situation signals a qualitative difference between the present SSL statistics and that of uncorrelated fermions representing a normal Fermi-liquid state. Abstract Published by the Jagiellonian University 2026 authors
We discuss two different cases of strongly correlated fermions statistics. The first of them called that of the non-Fermi liquid (NFL), i.e., that of fermions with exclusion of doubly occupancies of quasimomentum states {k} and opposite spins (↑↓). The second is that of statistical spin liquid (SSL), in which the fermion spins hop around and mix with the holes (unoccupied) states. For both cases we calculate the system entropy and the corresponding statistical distribution function, analyzed for a two-dimensional square-lattice filling n∈[0,1] and relative temperature kBT/∣t∣, where t<0 is the nearest neighbor hopping integral. We are particularly interested in the situation when the system of itinerant fermions reduce to the Mott-insulator state for the half-filled band (n→1). Thislimiting situation signals a qualitative difference between the present SSL statistics and that of uncorrelated fermions representing normal Fermi-liquid state.
The Fermi liquid theory is a central concept in modern condensed matter physics used to describe conventional metals. A state of this universality class consists of well-defined quasiparticles, which occupy a finite number of states within a Fermi volume defined in momentum space. According to the Luttinger’s theorem, such a state encloses a Fermi volume proportional to the electron density modulo the filled bands if no symmetry is broken. In the past decades strong deviations from Fermi liquid theory have been observed in the scaling behavior of thermodynamic observables in different materials, among which are for instance cuprates and iron pnictides. This thesis is about two prototypical systems that can not be described by Fermi liquid theory. The first part of this work investigates two-dimensional effective models, which are in a Mott insulating state at half-filling and have a finite conductivity when doped with holes. In such a Mott insulating state, the charge carriers are strongly localized due to the Coulomb repulsion. Hence, strong correlations are assumed to have a strong impact on the formation of the ground state, also in the regime of small hole concentration. In a first project we have used a so-called spinon dopon mean-field theory to represent the two-dimensional Fermi-Hubbard model with strong on-site repulsive interaction in effective degrees of freedom, in which the holes can be embedded into a quantum spin liquid. The corresponding SU(2) invariant ground state belongs to the class of fractionalized Fermi liquids. In a second project we investigate a quantum dimer model, an effective model based on a Hilbert space spanned by short range singlets and bound states of holes and spins. The focus here is on the calculation of the hole-part of the electron spectral function by using exact diagonalization and its comparison with two analytic methods, a diagrammatic computation based on the Bethe-Salpeter equation and a so-called two-mode approximation. The electron spectral function shows a similar analytic form in momentum space between nodal and antinodal point when compared to results from photoemission spectroscopy experiments on cuprates. Furthermore, in a subsequent work we calculate the exact ground state of the quantum dimer model along a certain parameter line. In order to analyze the behavior of the elctron spectral function when increasing the density of holes, we investigate the Fermi-Hubbard model in a current project using a dynamical mean-field approach. To solve the 4-site cluster impurity problem, we use a numerical renormalization group approach. However, numerical limitations force us to restrict the analysis to spin-polarized baths. According to the spectral data, the system is similar to the SU(2) invariant case at half-filling in a Mott insulating state and posseses a momentum-selective energy gap at finite doping. The topology of the Fermi surface shows a Lifshitz transition when increasing the hole concentration. Here, the curvature of the Fermi surface changes from electron- to hole-like. For comparison we apply the dynamical mean-field theory also to the quantum dimer model and observe that the electron spectral functions at finite doping are qualitatively similar to that of the two-dimensional Fermi-Hubbard model. The second half of the work is about Tomonaga-Luttinger liquid theory, which is used to describe the low-energy effective degrees of freedom of one-dimensional systems. Here, we first discuss a conceptional extension of the operator-based bosonization theory for one-dimensional systems. This extension is especially suited for inhomogeneous one-dimensional systems. First, we investigate a one-dimensional system with a local interation potential and compute an exact solution of the single particle propagator at T = 0. The critical exponent of the single particle propagator has an unconventional form as a function of the microscopic Tomonaga-Luttinger parameters, which is not covered by the original Luttinger paradigm postulated by F. Duncan M. Haldane. In a second project on one-dimensional systems, we study the impact of scattering processes among bosonic low-energy excitations on the thermalization process. Such scattering processes are irrelevant on large length scales, however strongly affect the dynamics. In our analytic analysis we focus on a experimental setup, where a one-dimensional Bose gas is instantaneously splitted in two identical, however strongly correlated, halves of one-dimensional electronic systems. In the following, the corresponding non-equilibrium state runs through multiple regimes in time, such as a metastable prethermalization regime. However, above a certain threshold in time such scattering processes cause an effective thermalization of the system. In order to demonstrate this, we compute the kinetic equation in the Keldysh field integral formalism from a diagrammatic expansion based on a self-consistent Born approximation.
We investigate the single-band Hubbard model with random site energies in the strong-repulsion limit, as represented by the slave-boson formulation of the t-J model. It is essential to include the correlations between the slave-boson mean field and the disorder. This leads to the widening of the non-Fermi-liquid (``generalized Mott insulating'') region around half filling. In the Fermi-liquid regime we apply the renormalization-group method. The resulting phase diagram has superconducting, magnetic, and insulating phases. The disorder generally suppresses superconductivity and gives rise to the formation of localized magnetic moments.