| 1. |
- Granath, Mats, 1972, et al.
(författare)
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Discretized thermal Green’s functions
- 2012
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Ingår i: Annalen der Physik. - : Wiley - VCH Verlag GmbH. - 0003-3804 .- 1521-3889. ; 524:3-4, s. 147-152
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Tidskriftsartikel (refereegranskat)abstract
- We present a spectral weight conserving formalism for Fermionic thermal Green's functions that are discretized in imaginary time t and thus periodic in imaginary (Matsubara) frequency i pi n. The formalism requires a generalization of the Dyson equation G (G0, S) and the Baym-Kadanoff-Luttinger-Ward functional for the free energy beta O = G (G). A conformal transformation is used to analytically continue the periodized Matsubara Green's function to real frequencies in a way that conserves the discontinuity at t = 0 of the corresponding real-time Green's function. This allows numerical Green's function calculations of very high precision and it appears to give a well controlled convergent approximation in the t discretization. The formalism is tested on dynamical mean field theory calculations of the paramagnetic Hubbard model.
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| 2. |
- Granath, Mats, 1972, et al.
(författare)
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Distributional exact diagonalization formalism for quantum impurity models
- 2012
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Ingår i: Physical Review B. - : American Physical Society. - 1098-0121 .- 2469-9950 .- 2469-9969. ; 86:11
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Tidskriftsartikel (refereegranskat)abstract
- We develop a method for calculating the self-energy of a quantum impurity coupled to a continuous bath by stochastically generating a distribution of finite Anderson models that are solved by exact diagonalization, using the noninteracting local spectral function as a probability distribution for the sampling. The method enables calculation of the full analytic self-energy and single-particle Green's function in the complex frequency plane, without analytic continuation, and can be used for both finite and zero temperature at arbitrary fillings. Results are in good agreement with imaginary frequency data from continuous-time quantum Monte Carlo calculations for the single-impurity Anderson model and the two-orbital Hubbard model within dynamical mean-field theory (DMFT) as well as real frequency data for self-energy of the single-band Hubbard model within DMFT using the numerical renormalization group. The method should be applicable to a wide range of quantum impurity models and particularly useful when high-precision real frequency results are sought.
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| 3. |
- Granath, Mats, 1972, et al.
(författare)
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Modeling a striped pseudogap state
- 2010
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Ingår i: Physical Review B. - 1098-0121. ; 81:2
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Tidskriftsartikel (refereegranskat)abstract
- We study the electronic structure within a system of phase-decoupled one-dimensional superconductors coexisting with stripe spin and charge-density-wave order. This system has a nodal Fermi surface (Fermi arc) in the form of a hole pocket and an antinodal pseudogap. The spectral function in the antinodes is approximately particle-hole symmetric contrary to the gapped regions just outside the pocket. We find that states at the Fermi energy are extended whereas states near the pseudogap energy have localization lengths as short as the interstripe spacing. We consider pairing which has either local d-wave or s-wave symmetry and find similar results in both cases, consistent with the pseudogap being an effect of local pair correlations. We suggest that this state is a stripe-ordered caricature of the pseudogap phase in underdoped cuprates with coexisting spin-, charge-, and pair-density-wave correlations. Lastly, we also model a superconducting state which (1) evolves smoothly from the pseudogap state, (2) has a signature subgap peak in the density of states, and (3) has the coherent pair density concentrated to the nodal region.
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| 4. |
- Granath, Mats, 1972, et al.
(författare)
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Signatures of Coherent Electronic Quasiparticles in the Paramagnetic Mott Insulator.
- 2014
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 90
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Tidskriftsartikel (refereegranskat)abstract
- We study the Mott insulating state of the half-filled paramagnetic Hubbard model within dynamical mean field theory using a recently formulated stochastic and non-perturbative quantum impurity solver. The method is based on calculating the impurity self energy as a sample average over a representative distribution of impurity models solved by exact diagonalization. Due to the natural parallelization of the method, millions of poles are readily generated for the self energy which allows to work with very small pole-broadening $\eta$. Solutions at small and large $\eta$ are qualitatively different; solutions at large $\eta$ show featureless Hubbard bands whereas solutions at small $\eta\leq 0.001$ (in units of half bare band width) show a band of electronic quasiparticles with very small quasiparticle weight at the inner edge of the Hubbard bands. The validity of the results are supported by agreement within statistical error $\sigma_{\text{QMC}}\sim 10^{-4}$ on the imaginary frequency axis with calculations using a continuous time quantum Monte Carlo solver. Nevertheless, convergence with respect to finite size of the stochastic exact diagonalization solver remains to be rigourously established.
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| 5. |
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| 6. |
- Sabashvili, Andro, 1984, et al.
(författare)
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Bilayer graphene spectral function in the random phase approximation and self-consistent GW approximation
- 2013
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121. ; 88
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Tidskriftsartikel (refereegranskat)abstract
- 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. Consistent with previous studies RPA 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 the GW approximation the plasmaron becomes incoherent and peaks are replaced by much broader features. The deviation of the quasiparticle weight and mass renormalization from their noninteracting values is small which indicates that bilayer graphene is a weakly interacting system. The electron energy loss function, Im[−εq−1(ω)] shows a sharp plasmon mode in RPA which in the GW approximation becomes less coherent and thus consistent with the weaker plasmaron features in the corresponding single-particle spectral function.
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| 7. |
- Strand, Hugo, 1983, et al.
(författare)
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The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition
- 2011
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Ingår i: Phys. Rev. B. - : American Physical Society. - 1098-0121. ; 83:20
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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