Effect of propagator renormalization on the band gap of insulating solids

Iskakov, Sergei; Rusakov, Alexander A.; Zgid, Dominika; Gull, Emanuel

doi:10.1103/physrevb.100.085112

Cited by 32 publications

(32 citation statements)

References 82 publications

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“…This argument is useful from a formal perspective but offers little insight into T -linear resistivity at intermediate temperatures or the lack of slope change across the crossover T ∼ U . In this "weak coupling" limit, we approximate single-site DMFT using self-consistent second-order perturbation theory (GF2) [34][35][36][37]. Unlike bare second-order perturbation theory, GF2 is -derivable [38] and therefore thermodynamically consistent and symmetry conserving [39,40], implying that thermodynamic relations and conservation laws are intrinsically satisfied.…”

Section: High-temperature Limitmentioning

confidence: 99%

Slope invariant T -linear resistivity from local self-energy

Cha

Patel

Gull

et al. 2020

Phys. Rev. Research

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A theoretical understanding of the enigmatic linear-in-temperature (T) resistivity, ubiquitous in strongly correlated metallic systems, has been a long sought-after goal. Furthermore, the slope of this robust T-linear resistivity is also observed to stay constant through crossovers between different temperature regimes: a phenomenon we dub "slope invariance." Recently, several solvable models with T-linear resistivity have been proposed, putting us in an opportune moment to compare their inner workings in various explicit calculations. We consider two strongly correlated models with local self-energies that demonstrate T linearity: a lattice of coupled Sachdev-Ye-Kitaev models and the Hubbard model in single-site dynamical mean-field theory. We find that the two models achieve T linearity through distinct mechanisms at intermediate temperatures. However, we also find that these mechanisms converge to an identical form at high temperatures. Surprisingly, both models exhibit "slope invariance" across the two temperature regimes. Thus not only do we reveal some of the diversity in the theoretical inner workings that can lead to T-linear resistivity, but we also establish that different mechanisms can result in "slope invarance."

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Section: High-temperature Limitmentioning

confidence: 99%

Slope invariant T -linear resistivity from local self-energy

Cha

Patel

Gull

et al. 2020

Phys. Rev. Research

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“…Self-consistent second order Green's function theory (GF2) is a second order perturbation theory which renormalizes the Green's function [24][25][26][27][28][29][30][31]. Self-consistent GW [15,17,[21][22][23] further renormalizes the interaction.…”

Section: Sparse Sampling Approach To Solving Diagrammatic Equationsmentioning

confidence: 99%

“…Applications to low-energy effective model Hamiltonians include lattice Monte Carlo [5], dynamical mean-field theory [6] with its cluster [7], multi-orbital extensions [8,9], and diagrammatic extensions [10][11][12], and diagrammatic or continuous-time quantum Monte Carlo methods [13,14]. In the context of ab initio calculations of correlated materials, examples include the GW method [15][16][17][18][19][20][21][22][23], the self-consistent second order approximation (GF2) [24][25][26][27][28][29][30][31], variants of the dynamical mean field theory [8,[32][33][34][35][36], and the self-energy embedding theory [37][38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Sparse sampling approach to efficient ab initio calculations at finite temperature

Wallerberger

Chikano

et al. 2020

Phys. Rev. B

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Efficient ab initio calculations of correlated materials at finite temperature require compact representations of the Green's functions both in imaginary time and Matsubara frequency. In this paper, we introduce a general procedure which generates sparse sampling points in time and frequency from compact orthogonal basis representations, such as Chebyshev polynomials and intermediate representation (IR) basis functions. These sampling points accurately resolve the information contained in the Green's function, and efficient transforms between different representations are formulated with minimal loss of information. As a demonstration, we apply the sparse sampling scheme to diagrammatic GW and GF2 calculations of a hydrogen chain, of noble gas atoms and of a silicon crystal.arXiv:1908.07575v1 [cond-mat.str-el]

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“…The MP2 method is closely related to GF2 and uses the second order self energy [Eq. (17)] evaluated at the HF Green's function ) ]. Note however that the prefactors in the total energy differ 10,69 .…”

Section: Resultsmentioning

confidence: 99%

Legendre-spectral Dyson equation solver with super-exponential convergence

Dong

Zgid

Gull

et al. 2020

The Journal of Chemical Physics

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Quantum many-body systems in thermal equilibrium can be described by the imaginary time Green's function formalism. However, the treatment of large molecular or solid ab inito problems with a fully realistic Hamiltonian in large basis sets is hampered by the storage of the Green's function and the precision of the solution of the Dyson equation. We present a Legendre-spectral algorithm for solving the Dyson equation that addresses both of these issues. By formulating the algorithm in Legendre coefficient space, our method inherits the known faster-than-exponential convergence of the Green's function's Legendre series expansion. In this basis, the fast recursive method for Legendre polynomial convolution, enables us to develop a Dyson equation solver with quadratic scaling. We present benchmarks of the algorithm by computing the dissociation energy of the helium dimer He 2 within dressed second-order perturbation theory. For this system, the application of the Legendre spectral algorithm allows us to achieve an energy accuracy of 10 −9 E h with only a few hundred expansion coefficients. arXiv:2001.11603v2 [cond-mat.str-el] 5 Apr 2020

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Effect of propagator renormalization on the band gap of insulating solids

Cited by 32 publications

References 82 publications

Slope invariant T -linear resistivity from local self-energy

Slope invariant T -linear resistivity from local self-energy

Sparse sampling approach to efficient ab initio calculations at finite temperature

Legendre-spectral Dyson equation solver with super-exponential convergence

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