13ª Semana Integrada do Instituto de Física de São Carlos

The time-dependent real-space numerical renormalization group formulation

21 de ago. de 2023 14:00

1h 30m

Salão de Eventos USP

Prêmio YPM 14h00 - 15h30

Descrição

Interest in the non-equilibrium properties of quantum devices has attracted much attention to time-dependent properties of strongly correlated electronic systems. In Kondo systems and analogous impurity problems, the description of the long-time behavior poses challenges. The Numerical Renormalization Group (NRG) method, a procedure that yields essentially exact results for the equilibrium thermodynamically, excitation, and transport properties of such systems, has proved less reliable in this context. The computed time-dependent curves are plagued by artificial oscillations, direct consequences of the logarithmic discretization at the heart of the NRG construction. Here, we adopt a similar approach, one that is nonetheless more flexible: the recently proposed real-space formulation dubbed eNRG. (1) We calculate the time-dependent photocurrent in a simple X-ray photoemission spectroscopy (XPS) process: the photoejection of a core electron from a simple metal. Our eNRG construction starts out with a unidimensional lattice with a coupling τ between neighboring sites - a tight-binding Hamiltonian. To define the final-state Hamiltonian, we apply a suddenly created potential to one of the lattice sites, which models the electrostatic interaction with the core hole resulting from the photoejection. The resulting spectrum comprises a bound state and uniformly phase-shifted extended states. To eliminate the artifacts of the discretization, we compare two smoothing procedures: (i) randomization of the couplings τ, in analogy with Micklitz et al, and (ii) uniform displacement of the conduction levels. (2) In excellent agreement with physical expectations, the resulting photocurrents oscillate with the energy required to excite an electron from the bound state to the Fermi level and decay with the Doniach-Sunjic power law. (3)

Referências

1 FERRARI, A. L.; OLIVEIRA, L. N. Real-space numerical renormalization group computation of transport properties in side-coupled geometry. Physical Review B, v. 106, n. 7, p. 075129-1-075129-34, Aug. 2022.

2 MICKLITZ, T.; MORNINGSTAR, A.; ALTLAND, A.; HUSE, D. A. Emergence of Fermi’s Golden Rule. Physical Review Letters, v. 129, n. 14, p. 140402-1-140402-6, Sept. 2022.

3 DONIACH, S; SUNJIC, M. Many-electron singularity in X-ray photoemission and X-ray line spectra from metals. Journal of Physics C, v. 3, n. 2, p. 285-291, Feb. 1970.