We describe a quantum simulator for the Hubbard-Holstein model (HHM), comprising two dressed Rydberg atom species held in a monolayer by independent painted potentials, predicting that boson-mediated preformed pairing and Berezinskii-Kosterlitz-Thouless (BKT) transition temperatures are experimentally accessible. The HHM is important for modeling the essential physics of unconventional superconductors. Experimentally realizable quantum simulators for HHMs are needed (1) since HHMs are difficult to solve numerically and analytically, (2) to explore how competition between electron-phonon interactions and strong repulsion affects pairing in unconventional superconductors, and (3) to understand the role of boson-mediated local pairing in pseudogaps and fermion condensates. We propose and study a quantum simulator for the HHM, using optical lattices, painted using zeros in the ac Stark shift, to control two Rydberg atom species independently within a monolayer. We predict that interactions are sufficiently tunable to probe (1) both HHMs and highly unconventional phonon-mediated repulsions, (2) the competition between intermediate-strength phonon- and Coulomb-mediated interactions, and (3) BKT transitions and preformed pairing that could be used to examine key hypotheses related to the pseudogap. We discuss how the quantum simulator can be used to investigate boson-mediated pairing and condensation of fermions in unconventional superconductors.
We extend the dynamical vertex approximation (D
ΓA), in its most commonly used ladder-version, to systems with retarded electronic interactions. Such an extended scheme, which we name "dynamical-
U D
ΓA", allows us to study strongly interacting electrons coupled to bosons including non-local spatial correlations on all length scales on top of the purely local ones captured by dynamical mean-field theory. We demonstrate the applicability of the method in the specific case of the coupling to a single dispersionless phononic mode, by studying the Hubbard-Holstein model on the square and cubic lattices, focusing on regimes of sizable Hubbard interactions where strong electronic correlations compete with phonon-mediated interactions. As illustrative examples, we consider the antiferromagnetic phase in the three-dimensional model and the d-wave superconductor in two dimensions, analyzing the effect of the electron-phonon coupling, including its frequency dependence, on both instabilities.
Abstract We explore the quantum phase transitions between two ordered states in the infinite dimensional Hubbard–Holstein model at half filling. Our study is based on the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG), which allows us to handle both strong electron–electron and strong electron–phonon interactions. The transition line is characterized by an effective electron–electron interaction. Depending on this effective interaction and the phonon frequency ω0 one finds either a continuous transition or discontinuous transition. Here, the analysis focuses on the behavior of the system when the electron–electron repulsion U and the phonon‐mediated attraction λ are equal. We first discuss the adiabatic and antiadiabatic limiting cases. For finite ω0 we study the differences between the antiferromagnetic (AFM) and charge order, and find that when present the AFM state has a lower energy on the line.