On Strongly Correlated Eelectrons in Metals

A procedure, dedicated to superconductivity, is extended to study the properties of interacting electrons in normal metals in the thermodynamic limit. Each independent-electron band is shown to split into two correlated-electron bands. Excellent agreement is achieved with Bethe's wave-function for the one-dimensional Hubbard model. The groundstate energy, reckoned for the two-dimensional Hubbard Hamiltonian, is found to be lower than values, obtained thanks to the numerical methods. This analysis applies for any spatial dimension and temperature.

Mechanisms

This chapter introduces the general concepts of pair correlation, and superconductivity as a strong non-adiabatic phenomenon. Phonon, electronic, and magnetic mechanisms play the major roles; each of them can serve as the origin of the superconducting state. Speaking of the phonon mechanism, it is essential that an explicit expression for Tc depend on the intensity of the electron–phonon interaction. In principle, the electron–phonon mechanism can provide high values of Tc, up to room temperature. Pioneering work by Little, who introduced the electronic mechanism, is described. The mechanism has been analysed for one-dimensional, two-dimensional, and three-dimensional systems. The plasmon mechanism can play a role for layered materials. The superconducting state can be provided by magnetic degrees of freedom. The band limit with spin fluctuations and the regime of strong electron correlations are described. The Hubbard Hamiltonian and the t − J model are the ingredients of the approach.

Magnetoelectric Coupling on the Fused Azulene Oligomers

<div><div><div><p>The global magnetic phase diagram for fused azulene oligomers is obtained by using a fermionic Hubbard Hamiltonian, a intermediate model between the molecular (Pariser-Parr-Pople empiric Hamiltonian) and spin-1/2 antiferromagnetic Heisenberg approaches. As a function of the on-site coulomb repulsion and the oligomer size we show that fused azulene transitions from a singlet (S = 0) to a higher-spin (S = 1, 2, 3) ground state. Near the quantum magnetic phase transition the electric dipole moment, present on fused azulene molecules, couples with the magnetic moment leading to a divergent magnetoelectric susceptibility at the boundary lines of the magnetic phase diagram. These spontaneous electric and magnetic polarizations, together with the magnetoelectric coupling between them, indicate that fuzed azulene molecules are potentially strong candidates for purely organic multiferroic materials.</p></div></div></div>

Magnetoelectric Coupling on the Fused Azulene Oligomers

<div><div><div><p>The global magnetic phase diagram for fused azulene oligomers is obtained by using a fermionic Hubbard Hamiltonian, a intermediate model between the molecular (Pariser-Parr-Pople empiric Hamiltonian) and spin-1/2 antiferromagnetic Heisenberg approaches. As a function of the on-site coulomb repulsion and the oligomer size we show that fused azulene transitions from a singlet (S = 0) to a higher-spin (S = 1, 2, 3) ground state. Near the quantum magnetic phase transition the electric dipole moment, present on fused azulene molecules, couples with the magnetic moment leading to a divergent magnetoelectric susceptibility at the boundary lines of the magnetic phase diagram. These spontaneous electric and magnetic polarizations, together with the magnetoelectric coupling between them, indicate that fuzed azulene molecules are potentially strong candidates for purely organic multiferroic materials.</p></div></div></div>

Quasistatic transfer protocols for atomtronic superfluid circuits

Quasi-static protocols for systems that feature a mixed phase-space with both chaos and quasi-regular regions are beyond the standard paradigm of adiabatic processes. We focus on many-body system of atoms that are described by the Bose–Hubbard Hamiltonian, specifically a circuit that consists of bosonic sites. We consider a sweep process: slow variation of the rotation frequency of the device (time dependent Sagnac phase). The parametric variation of phase-space topology implies that the quasi-static limit is not compatible with linear response theory. Detailed analysis is essential in order to determine the outcome of such transfer protocol, and its efficiency.

Ultracold Bosons on a Regular Spherical Mesh

Here, the zero-temperature phase behavior of bosonic particles living on the nodes of a regular spherical mesh (“Platonic mesh”) and interacting through an extended Bose-Hubbard Hamiltonian has been studied. Only the hard-core version of the model for two instances of Platonic mesh is considered here. Using the mean-field decoupling approximation, it is shown that the system may exist in various ground states, which can be regarded as analogs of gas, solid, supersolid, and superfluid. For one mesh, by comparing the theoretical results with the outcome of numerical diagonalization, I manage to uncover the signatures of diagonal and off-diagonal spatial orders in a finite quantum system.

Unitary unfoldings of a Bose–Hubbard exceptional point with and without particle number conservation

The conventional non-Hermitian but P T -symmetric three-parametric Bose–Hubbard Hamiltonian H ( γ , v , c ) represents a quantum system of N bosons, unitary only for parameters γ , v and c in a domain D . Its boundary ∂ D contains an exceptional point of order K (EPK; K = N + 1) at c = 0 and γ = v , but even at the smallest non-vanishing parameter c ≠ ~0 the spectrum of H ( v , v , c ) ceases to be real, i.e. the system ceases to be observable. In this paper, the question is inverted: all of the stable, unitary and observable Bose–Hubbard quantum systems are sought which would lie close to the phenomenologically most interesting EPK-related dynamical regime. Two different families of such systems are found. Both of them are characterized by the perturbed Hamiltonians H ( λ ) = H ( v , v , 0 ) + λ V for which the unitarity and stability of the system is guaranteed. In the first family the number N of bosons is assumed conserved while in the second family such an assumption is relaxed. Attention is paid mainly to an anisotropy of the physical Hilbert space near the EPK extreme. We show that it is reflected by a specific, operationally realizable structure of perturbations λ V which can be considered small.