Quantum phase transition in the two-band hubbard model

The interaction between itinerant and Mott localized electronic states in strongly correlated materials is studied within dynamical mean field theory in combination with the numerical renormalization group method. A novel nonmagnetic zero temperature quantum phase transition is found in the bad-metallic orbital-selective Mott phase of the two-band Hubbard model, for values of the Hund's exchange which are relevant to typical transition metal oxides.     

First-order pairing transition and single-particle spectral function in the attractive hubbard model

A dynamical mean-field theory analysis of the attractive Hubbard model in the normal phase is carried out upon restricting to solutions where superconducting order is not allowed. A clear first-order pairing transition as a function of the coupling takes place at all the electron densities out of half filling between a Fermi liquid, stable for UU(c), and it is accompanied by phase separation. The spectral function in the metallic phase is constituted by a low-energy structure around the Fermi level, which disappears discontinuously at U = U(c), and two high-energy features (Hubbard bands), which persist in the insulating phase.     

Dynamical mean-field theory for pairing and spin gap in the attractive hubbard model

We solve the attractive Hubbard model for arbitrary interaction strengths within dynamical mean-field theory. We compute the transition temperature for superconductivity and analyze electron pairing in the normal phase. The normal state is a Fermi liquid at weak coupling and a non-Fermi-liquid state with a spin gap at strong coupling. Away from half filling, the quasiparticle weight vanishes discontinuously at the transition between the two normal states.     

d-wave superconductivity in the hubbard model

The superconducting instabilities of the doped repulsive 2D Hubbard model are studied in the intermediate to strong coupling regime with the help of the dynamical cluster approximation. To solve the effective cluster problem we employ an extended noncrossing approximation, which allows for a transition to the broken symmetry state. At sufficiently low temperatures we find stable d-wave solutions with off-diagonal long-range order. The maximal T(c) approximately 150 K occurs for a doping delta approximately 20% and the doping dependence of the transition temperatures agrees well with the generic high- T(c) phase diagram.     

Quantum simulator for the hubbard model with long-range coulomb interactions using surface acoustic waves

An experimental scheme for a quantum simulator of strongly correlated electrons is proposed. Our scheme employs electrons confined in a two-dimensional electron gas in a GaAs/AlGaAs heterojunction. Two surface acoustic waves are then induced in the substrate, creating a two-dimensional "egg-carton" potential. The dynamics of the electrons in this potential are described by a Hubbard model with long-range Coulomb interactions. Estimates of the Hubbard parameters suggest that observations of quantum phase transition phenomena are within experimental reach.     

Spectral functions in the hubbard model with half-filling

Under the assumption of long-range antiferromagnetic order at low temperatures, the spectral functions and the density of states are calculated in the two-dimensional Hubbard model with half-filling in the Hubbard-I approximation. The results are compared with the data obtained using an exact numerical technique, namely, the quantum Monte Carlo method. The influence of hopping to the next-to-nearest neighbor on the formation of the electronic structure is considered.     

Pseudogap and antiferromagnetic correlations in the hubbard model

Using the dynamical cluster approximation and quantum Monte Carlo simulations we calculate the single-particle spectra of the Hubbard model with next-nearest neighbor hopping . In the underdoped region, we find that the pseudogap along the zone diagonal in the electron doped systems is due to long-range antiferromagnetic correlations. The physics in the proximity of (0, pi) is dramatically influenced by t' and determined by the short range correlations. The effect t' of on the low-energy angle-resolved photoemission spectroscopy spectra is weak except close to the zone edge. The short range correlations are sufficient to yield a pseudogap signal in the magnetic susceptibility and produce a concomitant gap in the single-particle spectra near (pi, pi/2), but not necessarily at a location in the proximity of the Fermi surface.     

Exact solution of the simplified hubbard model

We present the exact solution of the simplified Hubbard model in which only one kind of electrons can hop and this quantum mechanical hopping of electrons is assumed to be unconstrained. It is shown that the model still behaves nontrivially, although it no longer depends on the lattice structure and the dimensionality of the system. For this case we find: (i) a gap in the ground state energy always exists at the half-filled band point (n=1), (ii) a preferred magnetic state atn=1 and largeU is a total spin singlet, (iii)U-dependence of the ground state energy has qualitatively the same form as one of the conventional Hubbard model with the (t ²/U)-behavior at largeU. A phase diagram of the model is discussed.     

Quantum size effects in adatom island decay

The decay of hexagonal Ag adatom islands on top of larger Ag adatom islands on a Ag(111) surface is followed by a fast-scanning tunneling microscope. Islands do not always show the expected increase in decay rate with decreasing island size. Rather, distinct quantum size effects are observed where the decay rate decreases significantly for islands with diameters of 6, 9.3, 12.6, and 15.6 nm. We show that electron confinement of the surface state electrons is responsible for this enhancement of the detachment barrier for adatoms from the island edge.     

Quantum size effects in the polarizability of carbon fullerenes

We investigate the size-dependent dielectric response of carbon fullerenes with up to 3840 atoms in the framework of the linear response theory. Our results suggest a significant polarizability enhancement due to quantum size effects with respect to classical or semiclassical calculations. The accuracy of our results, based on a parametrized Hamiltonian, is verified by ab initio time dependent density functional calculations for smaller fullerenes. Our findings underline the importance of quantum effects in the electronic response of nano- and mesoscopic systems.     

Possible lattice distortions in the hubbard model for graphene

The Hubbard model on the honeycomb lattice is a well-known model for graphene. Equally well known is the Peierls type of instability of the lattice bond lengths. In the context of these two approximations we ask and answer the question of the possible lattice distortions for graphene in zero magnetic field. The answer is that in the thermodynamic limit only periodic, reflection-symmetric distortions are allowed and these have at most 6 atoms per unit cell as compared to two atoms for the undistorted lattice.     

Disorder effects in the BCS-BEC crossover region of the attractive Hubbard model

We study the disorder effects upon superconducting transition temperature T _c and the number of local pairs within the attractive Hubbard model in the combined Nozieres-Schmitt-Rink and DMFT + Σ approximations. We analyze the wide range of attractive interaction U, from the weak coupling region, where instability of the normal phase and superconductivity are well described by the BCS model, to the limit of strong coupling, where superconducting transition is determined by Bose-Einstein condensation of compact Cooper pairs, forming at temperatures much higher than superconducting transition temperature. It is shown that disorder can either suppress T _c in the weak coupling limit, or significantly enhance T _c in the case of strong coupling. However, in all cases we actually prove the validity of generalized Anderson theorem, so that all changes in T _c are related to change in the effective bandwidth due to disorder. Similarly, disorder effects on the number of local pairs are only due to these band-broadening effects.     

Quantum size effects in Friedel oscillations inside films

An analytical formula of density oscillations is found for metallic films of finite thickness. The result shows that the quantum size effect on density oscillations is surprisingly more evident in the middle of the film. As a result, the density oscillations in a finite film cannot be regarded as a simple addition of the two sets of Friedel oscillations for half-infinite metal no matter how thick the film is. This analytical result is confirmed by our numerical jellium-model computation. Such quantum size effect should exist in all the electron-mediated interactions that are driven by the Friedel oscillations. As an example, we indeed find it also exists in Ruderman–Kittel–Kasuya–Yosida interactions inside films.     

Renormalization group approach to the one-dimensional hubbard model

An approximate decimation method is applied to the one-dimensional half-filled Hubbard model. The specific heat, the entropy and the magnitude of local moments are calculated. The results are in good agreement with those obtained by Shiba at high temperatures.     

Quantum size effects and band structure in InSb

Quantum Size Effects (Q.S.E.) in InSb films have been detected by different experimental procedures.The work function dependence on thickness obtained from photoelectric emission threshold measurements is compared with prior results obtained with the retarding potential method. With both methods, the measured work function values are comparable. They are less than the corresponding bulk values, conforming to current theoretical predictions.The interband energy gap has been determined from photoelectric absorption band edge data: its value differs with respect to the bulk one, by the location of the first allowed energy subband in the conduction band due to the presence of Q.S.E.Some evidence is given for absence of a band structure dependence on Q.S.E.