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(Online) Taking locality to the next level : vertex-based extensions of DMFT and their application

Thomas Schäfer, CPHT, Ecole Polytechnique

Strong correlations are almost a guarantor for the emergence of intriguing physics with the Mott metal-to-insulator transition, cuprate superconductivity and quantum criticality as famous examples. The advance of the dynamical mean field-theory (DMFT) revolutionized their theoretical description in being able to treat quantum correlations exactly, while spatial correlations are only included on a mean-field level. The recent development of diagrammatic extensions of DMFT, based on vertex functions, aims at including these spatial fluctuations in order to describe regimes of strong correlations, where this type of fluctuations is substantial (e.g. in the vicinity of phase transitions).

In this talk I will review some of the recent developments of cutting-edge methods in the DMFT framework. First, I will present a synopsis of basically all the available methods for the Hubbard model on a square lattice in an arguably simple regime of small interaction, which, despite its simplicity, exhibits a series of salient physical crossovers [1,2] : upon cooling from the high-temperature incoherent regime, coherent quasiparticles are formed below T_QP. At lower T, magnetic correlations stemming from the antiferromagnetically ordered phase at T=0 are gradually enhanced, resulting in the opening of an electronic (pseudo-)gap at T_∗. In the second part of the talk, I will review the application of the dynamical vertex approximation (DΓA) on the Hubbard model and the periodic Anderson model for magnetic classical and quantum criticality. In the three-dimensional Hubbard model, the DΓA critical exponents of the magnetic susceptibility and correlation length are determined, providing evidence for a significant violation of the prediction of the conventional Hertz-Millis-Moriya theory [3]. In the two-dimensional periodic Anderson model, one can trace its change in ground state from an antiferromagnet at low hybridizations between d- and f-electrons to a paramagnetic Kondo insulating phase, resembling the famous Doniach phase diagram. Eventually, there, I will show the evolution of the (classical and quantum) critical exponents of the magnetic susceptibility, which are changing from the one of free spins γ = 1 to γ = 2 in the quantum critical regime [4].

[1] T. Schäfer, et al., in preparation (2020).
[2] F. Šimkovic, et al., Phys. Rev. Lett. 124, 017003 (2020).
[3] T. Schäfer, A. A. Katanin, K. Held, and A. Toschi, Phys. Rev. Lett. 119, 046402 (2017).
[4] T. Schäfer, A. A. Katanin, M. Kitatani, A. Toschi, K. Held, Phys. Rev. Lett. 122, 227201 (2019).


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