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In this review we present results of our theoretical study of charge and spin ordering in strongly correlated electron systems obtained within various generalizations of the Falicov-Kimball model. The primary goal of this study was to…
Free electrons provide a powerful tool to probe material properties at atomic-scale spatial resolution. Recent advances in ultrafast electron microscopy enable the manipulation of free electron wavefunctions using laser pulses. It would be…
We argue that the Anderson and Kondo models turn out to be irrelevant for the description of some strongly correlated electron systems and we suggest the mechanism for the formation of many-body states (heavy fermions) being an alternative…
A key notion in heavy-fermion systems is the entanglement between conduction electrons and localized spin degrees of freedom. To study these systems from this point of view, we compute the mutual information in a ferromagnetic and…
When an electronic system is subjected to a sufficiently strong magnetic field that the cyclotron energy is much larger than the Fermi energy, the system enters the "extreme quantum limit" (EQL) and becomes susceptible to a number of…
Insulating states can be topologically nontrivial, a well-established notion that is exemplified by the quantum Hall effect and topological insulators. By contrast, topological metals have not been experimentally evidenced until recently.…
A quantum system of particles can exist in a localized phase, exhibiting ergodicity breaking and maintaining forever a local memory of its initial conditions. We generalize this concept to a system of extended objects, such as strings and…
The quantum Hall ferromagnet at filling fraction $\nu = 1$ has some unusual properties due to the remarkable identity between the topological density of a spin distortion and the associated electrical charge density. We investigate the…
Quantum phase transitions are ubiquitous in many exotic behaviors of strongly-correlated materials. However the microscopic complexity impedes their quantitative understanding. Here, we observe thoroughly and comprehend the rich…
Effective dynamics of conduction electrons in antiferromagnetic (AFM) materials with slowly varying spin texture is developed via non-Abelian gauge theory. Quite different from the ferromagnetic (FM) case, the spin of a conduction electron…
The transition into a strongly-correlated regime of 3 fermions trapped in a one-dimensional harmonic potential is investigated. This interesting, but little-studied system, allows us to identify characteristic features of the regime, some…
This short review presents a few case studies of finite electron systems for which strong correlations play a dominant role. In simple metal clusters, the valence electrons determine stability and shape of the clusters. The ionic skeleton…
Single electron tunneling is studied in a many electron quantum dot in high magnetic fields. For such a system multiple transitions of the spin configuration are theoretically predicted. With a combination of spin blockade and Kondo effect…
Originally the Kondo effect describes a scattering mechanism of electrons in metals that have defects with internal quantum mechanical degrees of freedom. The characteristic dynamic interplay between localized and itinerant states occurs in…
Strongly correlated systems of fermions have a number of exciting collective properties. Among them, the creation of a lattice that is occupied by doublons, i.e. two quantum particles with opposite spins, offers interesting electronic…
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…
Heavy fermion materials have recently attracted attention for their potential to combine topological protection with strongly correlated electron physics. To date, the ideas of topological protection have been restricted to the heavy…
Materials with correlated electrons often respond very strongly to external or internal influences, leading to instabilities and states of matter with broken symmetry. This behavior can be studied theoretically either by evaluating the…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the…
Semiconductor architectures hold promise for quantum information processing (QIP) applications due to their large industrial base and perceived scalability potential. Electron spins in silicon in particular may be an excellent architecture…