Polaron Crossover and Bipolaronic Metal-Insulator Transition in the Holstein model at half-filling

The evolution of the properties of a finite density electronic system as the electron-phonon coupling is increased are investigated in the Holstein model using the Dynamical Mean-Field Theory (DMFT). We compare the spinless fermion case, in which only isolated polarons can be formed, with the spinful model in which the polarons can bind and form bipolarons. In the latter case, the bipolaronic binding occurs through a metal-insulator transition. In the adiabatic regime in which the phonon energy is small with respect to the electron hopping we compare numerically exact DMFT results with an analytical scheme inspired by the Born-Oppenheimer procedure. Within the latter approach,a truncation of the phononic Hilbert space leads to a mapping of the original model onto an Anderson spin-fermion model. In the anti-adiabatic regime (where the phonon energy exceeds the electronic scales) the standard treatment based on Lang-Firsov canonical transformation allows to map the original model on to an attractive Hubbard model in the spinful case. The separate analysis of the two regimes supports the numerical evidence that polaron formation is not necessarily associated to a metal-insulator transition, which is instead due to pairing between the carriers. At the polaron crossover the Born-Oppenheimer approximation is shown to break down due to the entanglement of the electron-phonon state.Comment: 19 pages, 15 figure

Electronic correlations stabilize the antiferromagnetic Mott state in Cs3_3C60_{60}

Cs$_3$C$_{60}$ in the A15 structure is an antiferromagnet at ambient pressure in contrast with other superconducting trivalent fullerides. Superconductivity is recovered under pressure and reaches the highest critical temperature of the family. Comparing density-functional calculations with generalized gradient approximation to the hybrid functional HSE, which includes a suitable component of exchange, we establish that the antiferromagnetic state of Cs$_3$C$_{60}$ is not due to a Slater mechanism, and it is stabilized by electron correlation. HSE also reproduces the pressure-driven metalization. Our findings corroborate previous analyses suggesting that the properties of this compound can be understood as the result of the interplay between electron correlations and Jahn-Teller electron-phonon interaction.Comment: 4 pages, 3 figure

Lattice approaches to dilute Fermi gases: Legacy of broken Galilean invariance

In the dilute limit, the properties of fermionic lattice models with short-range attractive interactions converge to those of a dilute Fermi gas in continuum space. We investigate this connection using mean-field and we show that the existence of a finite lattice spacing has consequences down to very small densities. In particular we show that the reduced translational invariance associated to the lattice periodicity has a pivotal role in the finite-density corrections to the universal zero-density limit. For a parabolic dispersion with a sharp cut-off, we provide an analytical expression for the leading-order corrections in the whole BCS-BEC crossover. These corrections, which stem only from the unavoidable cut-off, contribute to the leading-order corrections to the relevant observables. In a generic lattice we find a universal power-law behavior $n^{1/3}$ which leads to significant corrections already for small densities. Our results pose strong constraints on lattice extrapolations of dilute Fermi gas properties.Comment: 10 pages, 7 figure

Polaron Crossover and Bipolaronic Metal-Insulator Transition in the half- filled Holstein model

The formation of a finite density multipolaronic state is analyzed in the context of the Holstein model using the Dynamical Mean-Field Theory. The spinless and spinful fermion cases are compared to disentangle the polaron crossover from the bipolaron formation. The exact solution of Dynamical Mean-Field Theory is compared with weak-coupling perturbation theory, non-crossing (Migdal), and vertex correction approximations. We show that polaron formation is not associated to a metal-insulator transition, which is instead due to bipolaron formation.Comment: 4 pages, 5 figure

Antiferromagnetic integer-spin chains in a staggered magnetic field: approaching the thermodynamic limit through the infinite-size DMRG

We investigate the behavior of antiferromagnetic integer-spin chains in a staggered magnetic field, by means of the density-matrix renormalization group, carefully addressing the role of finite-size effects within the Haldane phase at small fields. In the case of spin S=2, we determine the dependence of the groundstate energy and magnetization on the external field, in the thermodynamic limit, and show how the peculiar finite-size behavior can be connected with the crossover in the groundstate from a spin liquid to a polarized N\'eel state.Comment: 7 pages, 5 figure

A darkless space-time

In cosmology it has become usual to introduce new entities as dark matter and dark energy in order to explain otherwise unexplained observational facts. Here, we propose a different approach treating spacetime as a continuum endowed with properties similar to the ones of ordinary material continua, such as internal viscosity and strain distributions originated by defects in the texture. A Lagrangian modeled on the one valid for simple dissipative phenomena in fluids is built and used for empty spacetime. The internal "viscosity" is shown to correspond to a four-vector field. The vector field is shown to be connected with the displacement vector field induced by a point defect in a four-dimensional continuum. Using the known symmetry of the universe, assuming the vector field to be divergenceless and solving the corresponding Euler-Lagrange equation, we directly obtain inflation and a phase of accelerated expansion of spacetime. The only parameter in the theory is the "strength" of the defect. We show that it is possible to fix it in such a way to also quantitatively reproduce the acceleration of the universe. We have finally verified that the addition of ordinary matter does not change the general behaviour of the model.Comment: 13 pages, 7 figures Typos; section V on Newtonian limit adde

Electron-phonon interaction in Strongly Correlated Systems

The Hubbard-Holstein model is a simple model including both electron-phonon interaction and electron-electron correlations. We review a body of theoretical work investigating the effects of strong correlations on the electron-phonon interaction. We focus on the regime, relevant to high-T_c superconductors, in which the electron correlations are dominant. We find that the electron-phonon interaction can still have important signatures, even if many anomalies appear, and the overall effect is far from conventional. In particular in the paramagnetic phase the effects of phonons are much reduced in the low-energy properties, while the high-energy physics can be strongly affected by phonons. Moreover, the electron-phonon interaction can still give rise to important effects, like phase separation and charge-ordering, and it assumes a predominance of forward scattering even if the bare interaction is assumed to be local (momentum independent). Antiferromagnetic correlations reduce the screening effects due to electron-electron interactions and revive the electron-phonon effects.Comment: 15 pages, 12 figure

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 is carried out. We focus on the normal state upon restricting to solutions where superconducting order is not allowed. Nevertheless a clear first-order pairing transition as a function of the coupling takes place at all the electron densities out of half-filling. The transition occurs between a Fermi liquid, stable for $U U_c$. The spectral function in the Fermi liquid phase is constituted by a low energy structure around the Fermi level (similar to the Kondo resonance of the repulsive half-filled model), which disappears discontinuously at $U=U_c$, and two high energy features (lower and upper Hubbard bands), which persist in the insulating phase.Comment: 5 pages, 3 figures, accepted for publication in Physical Review Letter