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We study the fidelity approach to quantum phase transitions (QPTs) and apply it to general thermal phase transitions (PTs). We analyze two particular cases: the Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of…
Upon increasing the electron density in a quantum wire, the one-dimensional electron system undergoes a transition to a quasi-one-dimensional state. In the absence of interactions between electrons, this corresponds to filling up the second…
We predict the new type of phase transition in quasi one-dimensional system of interacting electrons at high magnetic fields, the stabilization of a density wave which transforms a two dimensional open Fermi surface into a periodic chain of…
The Fermi liquid approach is applied to the problem of spontaneous violation of the four-fold rotational point-group symmetry ($C_4$) in strongly correlated two-dimensional electronic systems on a square lattice. The symmetry breaking is…
We review the theories of a few quantum phase transitions in two-dimensional correlated electron systems and discuss their application to the cuprate high temperature superconductors. The coupled-ladder antiferromagnet displays a transition…
We study generic features of open quantum systems embedded into a continuum of scattering wavefunctions and compare them with results discussed in optics. A dynamical phase transition may appear at high level density in a many-level system…
Classical stationary points of an analytic Hamiltonian induce singularities of the density of quantum energy levels and their flow with a control parameter in the system's infinite-size limit. We show that for a system with $f$ degrees of…
We study the effect of an external magnetic field in the Kondo regime of a double-quantum-dot system in which a strongly correlated dot (the "hanging dot") is coupled to a second, noninteracting dot that also bridges the gap between two…
By studying the quantum Hall effect of stationary states with high values of injected current using a von Neumann lattice representation, we found that broadening of extended state bands due to a Hall electric field occurs and causes the…
Quantum electronic matter has long been understood in terms of two limiting behaviors of electrons: one of delocalized metallic states, and the other of localized magnetic states. Understanding the strange metallic behavior which develops…
Excitons, Coulomb-driven bound states of electrons and holes, are typically composed of integer charges. However, in bilayer systems influenced by charge fractionalization, a more exotic form of interlayer exciton can emerge, where pairing…
The Dicke model exhibits a variety of phase transitions. The quantum phase transition from the normal phase to the super-radiant phase is marked by a dramatic change in the scaling of the participation ratio. We find that the ground state…
We study the transconductance for two coupled one-dimensional wires or edge states described by Luttinger liquid models. The wires are assumed to interact over a finite segment. We find for the interaction parameter $g=1/2$ that the drag…
This article examines the consequences of the existence of an upper particle momentum limit in quantum electrodynamics, where this momentum limit is the Planck momentum. The method used is Fourier analysis as developed already by Fermi in…
The linear and nonlinear transport through a multi-level lateral quantum dot connected to two leads is investigated using a generalized finite-$U$ slave-boson mean field approach. For a two-level quantum dot, our calculation demonstrates a…
The quantum-classical crossover from the Fermi liquid towards the Wigner solid is numerically revisited, considering small square lattice models where electrons interact via a Coulomb U/r potential. We review a series of exact numerical…
In this paper, we study the emergence of a Landauer transport regime from the quantum-mechanical dynamics of free electrons in a disordered tight-binding chain, which is coupled to finite leads with open boundaries. Both partitioned and…
Bound states in the continuum (BICs) are quantum states with normalizable wave functions and energies that lie within the continuous spectrum for which extended or dispersive states are also available. These special states, which have shown…
The chiral anomaly is a fundamental quantum mechanical phenomenon which is of great importance to both particle physics and condensed matter physics alike. In the context of QED it manifests as the breaking of chiral symmetry in the…
Short-range electron-electron interactions are incorporated into the network model of the integer quantum Hall effect. In the presence of interactions, the electrons, propagating along one link, experience exchange scattering off the…