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Competing inhomogeneous orders are a central feature of correlated electron materials including the high-temperature superconductors. The two- dimensional Hubbard model serves as the canonical microscopic physical model for such systems.…
This article is a review o over theory of superconductivity, which is constructed for systems with two overlapping energy bands at the Fermi surface and with arbitrary charge carrier density.There is taken into account all possible kinds of…
We note that the existence of physical states which are coherent superpositions of states with even and odd numbers of fermions means the existence, together with x,y,z,t, of additional spinor dimensions of space-time. A system with…
The Bardeen-Cooper-Schrieffer mechanism for superconductivity is a triumph of the theory of many-body systems. Implicit in its formulation is the existence of long-lived (quasi)particles, originating from the electronic building blocks of…
Since electronic and magnetic properties of many transition-metal oxides can be efficiently controlled by external factors such as the temperature, pressure, electric or magnetic field, they are regarded as promising materials for various…
As the dimensionality is reduced, the world becomes more and more interesting; novel and fascinating phenomena show up which call for understanding. Physics in one dimension is a fascinating topic for theory and experiment: for the former…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
Superconductivity and the normal state electrical resistivity which varies as $T^2$ are strongly enhanced near the compressibility and charge density wave instabilities in the electron-positive fermion gas. The additional screening from the…
The electronic structure of the high-Tc cuprates is studied in terms of "large-U" and "small-U" orbitals. A striped structure and three types of quasiparticles are obtained, polaron-like "stripons" carrying charge, "svivons" carrying spin,…
Controlling matter to simultaneously support multiple coupled properties is of fundamental and technological importance. For example, the simultaneous presence of magnetic and ferroelectric orders in multiferroic materials leads to enhanced…
We deal with a model for high-temperature superconductivity which maintains that in cuprates electrons running in the copper oxide layers, found in lattice of these materials, form spin-singlet bonds with electrons running in the…
The two dimensional system of electrons in a high magnetic field offers an opportunity to investigate a phase transition from a quantum liquid into a Wigner solid. Recent experiments have revealed an incipient composite fermion liquid in a…
Properties of strongly correlated two-dimensional (2D) electron systems in solids are studied on the assumption that these systems undergo a phase transition, called fermion condensation, whose characteristic feature is flattening of the…
Electron interactions are pivotal for defining the electronic structure of quantum materials. In particular, the strong electron Coulomb repulsion is considered the keystone for describing the emergence of exotic and/or ordered phases of…
A number of spectacular experimental anomalies\cite{li-2007,fujita-2005} have recently been discovered in certain cuprates, notably {\LBCO} and {\LNSCO}, which exhibit unidirectional spin and charge order (known as ``stripe order''). We…
The pairing temperature of superconducting thin films is expected to display, within the Bardeen-Cooper-Schrieffer theory, oscillations as a function of the film thickness. We show that the pattern of these oscillations switches between two…
We discuss the mechanisms of unconventional superconductivity and superfluidity in 3D and 2D fermionic systems with purely repulsive interaction at low densities. We construct phase diagrams of these systems and find the areas of the…
We study the applicability of composite fermion theory to electrons in two-dimensional parabolically-confined quantum dots in a strong perpendicular magnetic field in the limit of low Zeeman energy. The non-interacting composite fermion…
The Hubbard model is reformulated in terms of different ``colored'' fermion species for the electrons or holes at different lattice sites. Antiferromagnetic ordering or d-wave superconductivity can then be described in terms of…
Complex and correlated quantum systems with promise for new functionality often involve entwined electronic degrees of freedom. In such materials, highly unusual properties emerge and could be the result of electron localization. Here, a…