The effect of the strong intersite Coulomb correlations on the formation of the electron structure of the t-V-model has been studied. A qualitatively new result has been obtained which consists in the occurrence of a split-off band of the Fermi states. The spectral intensity of this band increases with the enhancement of a doping level and is determined by the mean-square fluctuation of the occupation numbers. This leads to the qualitative change in the structure of the electron density of states.
Flat band systems have recently attracted significant attention due to their instability under small perturbations, which can lead to the stabilization of many exotic quantum phases. We study a trimer ladder which shows a middle flat band in the absence of onsite Coulomb interaction. We investigate the quantum phases of the Hubbard model on this geometry using exact diagonalization, density matrix renormalization group, and perturbation theory. We construct a quantum phase diagram in the plane of the next-nearest-neighbor hopping parameter
t2 and onsite Coulomb interaction
U, revealing five distinct quantum phases. At low
U and moderate to high magnitude of
t2, the system exhibits metallic behavior, while at large
U and small magnitude of
t2, it transitions to a ferrimagnetic insulator phase, similar to those observed in certain trimer materials. In the small
t2 limit, the Fermi energy is in the flat band, leading to localization of the electrons within the trimer. At low
U and small magnitude of
t2, the flat band mechanism favors insulating ferrimagnetism, whereas at large
U, ferrimagnetic states emerge from singlet dimer formation between neighboring sites of a trimer and an isolated corner spin, which connect ferromagnetically. The insulating cell spin density wave phase displays an up-up--down-down spin configuration due to competing nearest-neighbor hopping
t1. Interestingly, in moderate
U and
∣t2∣>0.3, the ground state behaves like metallic Tomonaga-Luttinger liquid.
Abstract Systematic quantum chemical calculations were performed for the ground and a number of low-lying electronically excited doublet and quartet states of the rubidium trimer molecule. The obtained potential energy surfaces (PES), spin-orbit couplings (SOC) and electronic transition dipole moments (ETDM) can be useful for optimizing paths for laser synthesis, cooling and manipulation of stable ensembles of Rb3 molecules at ultralow temperatures. Ab initio calculations of the electronic structure of the homonuclear Rb3 molecule, in linear, isosceles triangle and equilateral triangle geometries, were performed using the multi-reference configuration interaction method, taking into account single and double excitations (M-R‑CISD) and with explicit dynamic correlation of only the three valence electrons. The structure of each atom was approximated using a nine-electron effective core potential (ECP28MDF), and molecular orbitals (MOs) were optimized using the spin averaged (over doublet and quartet states) multi-configuration self-consistent field (SA-CASSCF) method. Core–valence correlations between twenty-four subvalence electrons located on doubly occupied MOs and three valence electrons were implicitly taken into account using a one-electron angular momentum-independent Müller–Mayer core polarization potential (CPP). As a result of topological investigations at over 35 000 points, two dimensional PES, SOC, and ETDM functions were obtained and the geometric parameters Rb3 were found at which the most intense vertical transitions and the maximum influence of the SOC are expected.
We investigate the ground state (T = 0 K) of the one-dimensional symmetrical (n = 1) Hubbard model formalized in terms of the system of integral equations, which we previously obtained using the method of the generating functional of Green’s functions with the subsequent Legendre transformation. In a wide range of variations in the parameter of Coulomb interaction U, the following characteristics of the system have been calculated: the electron density of states, the electron band spectrum, the number of doubly occupied lattice sites, the localized magnetic moment, the correlator of the square of the longitudinal component of spin at a site,<S Z 2>, and the internal energy of the system. It has been shown that, for all U > 0, the model yields two solutions, i.e., an antiferromagnetic insulator and a paramagnetic insulator, in which there are no single-electron quasi-particles at the Fermi level. The energy of the paramagnetic solution in the region of U < 1.1 is considerably less than that of the antiferromagnetic solution for the case of U > 1.1, we have the opposite situation.
We show that the dipole-dipole interaction between three identical Rydberg atoms can give rise to bound trimer states. The microscopic origin of these states is fundamentally different from Efimov physics. Two stable trimer configurations exist where the atoms form the vertices of an equilateral triangle in a plane perpendicular to a static electric field. The triangle edge length typically exceeds R≈2 μm, and each configuration is twofold degenerate due to Kramers degeneracy. The depth of the potential wells and the triangle edge length can be controlled by external parameters. We establish the Borromean nature of the trimer states, analyze the quantum dynamics in the potential wells, and describe methods for their production and detection.
By use of the conservation laws a four-site Hubbard model coupled to a particle bath within an external magnetic field in z-direction was diagonalized. The analytical dependence of both the eigenvalues and the eigenstates on the interaction strength, the chemical potential and magnetic field was calculated. It is demonstrated that the low temperature behaviour is determined by a delicate interplay between many-particle states differing in electron number and spin if the electron density is away from half-filling. The grand partition sum is calculated and the specific heat, the susceptibility as well as various correlation functions and spectral functions are given in dependence of the interaction strength, the electron occupation and the applied magnetic field. For both the grand canonical and the canonical ensemble the high-temperature crossing points of the specific heat are calculated. Whereas in the weak correlation regime the universal value calculated by second order perturbation theory for several Hubbard systems being in the thermodynamic limit is confirmed, these crossing points vanish for intermediate to strong correlation.