Bilayer graphene spectral function in RPA and self-consistent GW

We calculate the single-particle spectral function for doped bilayer graphene in the low energy limit, described by two parabolic bands with zero band gap and long range Coulomb interaction. Calculations are done using thermal Green's functions in both the random phase approximation (RPA) and the fully self-consistent GW approximation. RPA (in line with previous studies) yields a spectral function which apart from the Landau quasiparticle peaks shows additional coherent features interpreted as plasmarons, i.e. composite electron-plasmon excitations. In GW the plasmaron becomes incoherent and peaks are replaced by much broader features. The deviation of the quasiparticle weight and mass renormalization from their non-interacting values is small which indicates that bilayer graphene is a weakly interacting system. The electron energy loss function, $Im[-\epsilon^{-1}_q(\omega)]$ shows a sharp plasmon mode in RPA which in GW approximation becomes less coherent and thus consistent with the weaker plasmaron features in the corresponding single-particle spectral function

The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition

We consider the finite temperature metal-insulator transition in the half filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A new method for calculating the Dynamical Mean Field Theory fixpoint surface in the phase diagram is presented and shown to be free from the convergence problems of standard forward recursion. The fixpoint equation is then analyzed using dynamical systems methods. On the fixpoint surface the eigenspectra of its Jacobian is used to characterize the hysteresis boundaries of the first order transition line and its second order critical end point. The critical point is shown to be a cusp catastrophe in the parameter space, opening a pitchfork bifurcation along the first order transition line, while the hysteresis boundaries are shown to be saddle-node bifurcations of two merging fixpoints. Using Landau theory the properties of the critical end point is determined and related to the critical eigenmode of the Jacobian. Our findings provide new insights into basic properties of this intensively studied transition.Comment: 11 pages, 12 figures, 1 tabl

The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition

We consider the finite temperature metal-insulator transition in the half filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A new method for calculating the Dynamical Mean Field Theory fixpoint surface in the phase diagram is presented and shown to be free from the convergence problems of standard forward recursion. The fixpoint equation is then analyzed using dynamical systems methods. On the fixpoint surface the eigenspectra of its Jacobian is used to characterize the hysteresis boundaries of the first order transition line and its second order critical end point. The critical point is shown to be a cusp catastrophe in the parameter space, opening a pitchfork bifurcation along the first order transition line, while the hysteresis boundaries are shown to be saddle-node bifurcations of two merging fixpoints. Using Landau theory the properties of the critical end point is determined and related to the critical eigenmode of the Jacobian. Our findings provide new insights into basic properties of this intensively studied transition.Comment: 11 pages, 12 figures, 1 tabl

Periodized Thermal Greens Functions and Applications

This work describes a new formalism for Fermionic thermal Greens functions that are discretized in imaginary time. The discretization makes the thermal Greens function periodic in imaginary (Matsubara) frequency space and requires a generalisation of the Dyson equation and Luttinger-Ward-Baym-Kadanoff functional. A Pade method is used to perform an analytic continuation of the periodized Matsubara Greens function to real frequencies which conserves the spectral weight and thus the discontinuity of the corresponding real time Greens function at t = 0. Due to the Matsubara Greens function periodicity, the discrete imaginary frequency space is relatively small which allows calculations at the extremely high precision which is necessary to perform a reliable Pade fit. We use the method to compute the single particle spectral function and energy loss function for doped bilayer graphene in the two-band limit, described by parabolic dispersion and Coulomb interaction. Calculations are performed in both the random phase approximation (RPA) and the fully self-consistent GW approximation. The formalism is also applied to dynamical mean field the- ory calculations using iterated perturbation theory (IPT) for the paramagnetic Hubbard model

The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition

We consider the finite temperature metal-insulator transition in the half filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A new method for calculating the Dynamical Mean Field Theory fixpoint surface in the phase diagram is presented and shown to be free from the convergence problems of standard forward recursion. The fixpoint equation is then analyzed using dynamical systems methods. On the fixpoint surface the eigenspectra of its Jacobian is used to characterize the hysteresis boundaries of the first order transition line and its second order critical end point. The critical point is shown to be a cusp catastrophe in the parameter space, opening a pitchfork bifurcation along the first order transition line, while the hysteresis boundaries are shown to be saddle-node bifurcations of two merging fixpoints. Using Landau theory the properties of the critical end point is determined and related to the critical eigenmode of the Jacobian. Our findings provide new insights into basic properties of this intensively studied transition