Nonequilibrium sum rules for the retarded self-energy of strongly correlated electrons

Turkowski, Volodymyr; Freericks, J. K.

doi:10.1103/physrevb.77.205102

Cited by 27 publications

(20 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…for the single-band Hubbard model in a paramagnetic state, where U is the on-site Coulomb repulsion and n is the electron density per spin [7]. The higher-order moments of the single-particle Green's function may impose further constraints for ∆ k and other parameters [69].…”

Section: Acknowledgmentsmentioning

confidence: 99%

Brillouin-zone integration scheme for many-body density of states: Tetrahedron method combined with cluster perturbation theory

Seki

Yunoki

2016

Phys. Rev. B

View full text Add to dashboard Cite

By combining the tetrahedron method with the cluster perturbation theory (CPT), we present an accurate method to numerically calculate the density of states of interacting fermions without introducing the Lorentzian broadening parameter η or the numerical extrapolation of η → 0. The method is conceptually based on the notion of the effective single-particle Hamiltonian which can be subtracted in the Lehmann representation of the single-particle Green's function within the CPT. Indeed, we show the general correspondence between the self-energy and the effective single-particle Hamiltonian which describes exactly the single-particle excitation energies of interacting fermions. The detailed formalism is provided for two-dimensional multi-orbital systems and a benchmark calculation is performed for the two-dimensional single-band Hubbard model. The method can be adapted straightforwardly to symmetry broken states, three-dimensional systems, and finitetemperature calculations.

show abstract

Section: Acknowledgmentsmentioning

confidence: 99%

Brillouin-zone integration scheme for many-body density of states: Tetrahedron method combined with cluster perturbation theory

Seki

Yunoki

2016

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…The moment sum rules have already been derived in equilibrium (Kornilovitch, 2002;R€ osch et al, 2007), but they actually hold true, unchanged, in nonequilibrium as well (Turkowski & Freericks, 2006;Turkowski & Freericks, 2008;Freericks & Turkowski, 2009;Freericks et al, 2013). With these sum rules, one can understand how the electron-phonon interaction responds to nonequilibrium driving and how different response functions will behave.…”

Section: Introductionmentioning

confidence: 84%

“…Unlike in the case of the Hubbard or Falicov-Kimball model, where the sum rules relate to constants or simple expectation values (Turkowski & Freericks, 2006;Turkowski & Freericks, 2008;Freericks & Turkowski, 2009), one can see here that one needs to know things like the average phonon coordinate and its fluctuations in order to find the moments. We will discuss this further later in this paper.…”

Section: Formalism For the Electronic Sum Rulesmentioning

confidence: 91%

See 1 more Smart Citation

Femtosecond Electron Imaging and Spectroscopy

Berz

Duxbury

Makino

et al. 2015

Advances in Imaging and Electron Physics

View full text Add to dashboard Cite

“…The time integrations in Equation (26) are performed over the three-branch complex time contour (see, e.g., [41][42][43] (27) This equation gives the exact expression for the XC potential in terms of the many-body XC self-energy and Green's function. This opens the door to controllable analytical approximations for v XC , in particular by using known analytical properties of the self-energy, such as its high-frequency dependence and different sum rules (see, for example, [61,62]). …”

Section: The Non-linear Response: a Possible Extension Of The Formalismmentioning

confidence: 99%

Towards TDDFT for Strongly Correlated Materials

2016

View full text Add to dashboard Cite

Abstract:We present some details of our recently-proposed Time-Dependent Density-Functional Theory (TDDFT) for strongly-correlated materials in which the exchange-correlation (XC) kernel is derived from the charge susceptibility obtained using Dynamical Mean-Field Theory (the TDDFT + DMFT approach). We proceed with deriving the expression for the XC kernel for the one-band Hubbard model by solving DMFT equations via two approaches, the Hirsch-Fye Quantum Monte Carlo (HF-QMC) and an approximate low-cost perturbation theory approach, and demonstrate that the latter gives results that are comparable to the exact HF-QMC solution. Furthermore, through a variety of applications, we propose a simple analytical formula for the XC kernel. Additionally, we use the exact and approximate kernels to examine the nonhomogeneous ultrafast response of two systems: a one-band Hubbard model and a Mott insulator YTiO 3 . We show that the frequency dependence of the kernel, i.e., memory effects, is important for dynamics at the femtosecond timescale. We also conclude that strong correlations lead to the presence of beats in the time-dependent electric conductivity in YTiO 3 , a feature that could be tested experimentally and that could help validate the few approximations used in our formulation. We conclude by proposing an algorithm for the generalization of the theory to non-linear response.

show abstract

Nonequilibrium sum rules for the retarded self-energy of strongly correlated electrons

Cited by 27 publications

References 44 publications

Brillouin-zone integration scheme for many-body density of states: Tetrahedron method combined with cluster perturbation theory

Brillouin-zone integration scheme for many-body density of states: Tetrahedron method combined with cluster perturbation theory

Femtosecond Electron Imaging and Spectroscopy

Towards TDDFT for Strongly Correlated Materials

Contact Info

Product

Resources

About