Revisiting the impurity Metal-Insulator transition at the heart of DMFT

Prof. Dr. Siddhartha Lal - Department of Physical Sciences, IISER Kolkata, India. November 10, 2022

Dynamical mean-field theory (DMFT) obtains an exact solution of the metal-insulator transition (MIT) of the ½-filled Hubbard model on the Bethe lattice with infinite coordination number, in terms of the local MIT of an Anderson impurity model that is hybridized with a conduction bath of correlated electrons whose properties (e.g., the electronic density of states) are determined self-consistently. The MIT is observed via the impurity/bath local spectral function, in terms of a dynamical transfer of spectral weight from the Kondo resonance at zero frequency to Hubbard sidebands at higher frequencies as the on-site Hubbard repulsion (U) on the Anderson impurity is tuned towards strong coupling. However, the numerical implementation of self-consistency precludes a deeper understanding of the physics mechanism responsible for the breakdown of the Kondo screening process, and the related dynamical spectral weight transfer. In meeting this goal, we develop a minimal impurity model by extending the standard Anderson impurity model to include an additional local spin exchange coupling between the impurity and the conduction bath, as well as a weak local on-site correlation in the conduction bath site just adjacent to the impurity. We analyse this extended Anderson impurity model by employing the recently developed unitary renormalization group (URG) method [1-4]. This reveals that local holon-doublon fluctuations on the bath sites nearby the impurity destabilise the local Fermi liquid metal phase, and lead to the emergence of the repulsion-driven local moment Mott insulating phase of the impurity. Interestingly, a local non-Fermi liquid metal is found to exist precisely at the transition, and marks a partial breakdown of the Kondo screening. We will present the understanding obtained of the well-studied phenomenology of the MIT within DMFT, as well as some novel predictions on the universal nature of the metal-insulator transition in this model. Implications for DMFT studies of more realistic models of strongly correlated electronic systems are considered.

References
1. A. Mukherjee and S. Lal. Nucl. Phys. B 960, 115170 (2020);
ibid, Nucl. Phys. B 960, 115163 (2020)
2. A. Mukherjee and S. Lal. New Journal of Physics. 22, 063007
(2020); ibid, New Journal of Physics. 22, 063008 (2020).
3. A. Mukherjee et al., Physical Review B 105, 085119 (2022)
4. S. Patra et al., arXiv:2205.00790

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