DMFT-QE Symposium: February 10th

Date


Talk 1:

Quantum embedding perspective of topological superconductivity in Rashba-Hubbard systems

Thomas Maier, Oak Ridge National Laboratory

Quantum embedding theories provide a powerful framework to study the effects of electron correlations in quantum materials by replacing the intractable many-body problem with a manageable dynamic mean-field problem that treats short-ranged correlations accurately within an effective cluster. In this talk, I will give an overview of the dynamic cluster approximation (DCA), a quantum embedding theory that uses coarse-graining of momentum space to embed the cluster in a self-consistent mean-field. After a general introduction of the method, I will discuss recent DCA calculations of a Rashba-Zeeman-Hubbard model that provides an interesting testing ground to study the interplay between strong electron interactions, spin-orbit coupling, and time-reversal symmetry breaking. I will discuss how electronic correlations and topology conspire to give rise to novel phenomena such as topological superconductivity, and how these interactions can be tuned to optimize the desired functionality.

Talk 2:

Solving the Mott Problem

Philip W. Phillips, University of Illinois Urbana-Champaign

I will show that Mott physics is controlled by the breaking of a hidden discrete Z2 symmetry of a Fermi liquid. The simplest Hamiltonian that exemplifies this symmetry breaking is the Hatsugai/Kohmoto (HK) model which was introduced in 1992 but was left for dead until its recent resurrection. I will show how this model can be amended to systematically include all the momentum scattering it leaves out but is necessary to describe the full Hubbard model. The procedure is simple: In a Brillouin zone with N momentum states place N/n Hubbard clusters each containing n-sites. Connect the clusters with twisted boundary conditions. What is surprising is that n does not have to be particularly large to obtain full Mott physics. Excellent agreement (within a percent) of the ground state/energy gap of the d=1 Bethe ansatz solution is already present at n = 8. The convergence to Hubbard, which scales as 1/n2, is due to the existence of the Z2 breaking fixed point. No local repulsive interactions destroy the fixed point. Quantitative agreement with state-of-the art simulationsalso persists for d=2. In fact, the general convergence is 1/n2d. Computation of the k-dependent occupancy shows a systematic violation of the Luttinger count which we show is due to zeros of the single-particle Green function. Finally, I show how this procedure can be used to make comparison with DMFT.

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