Phase diagram of the two-dimensional Hubbard-Holstein model

Over the past decades, a great deal of interest has been given to quasi-2D materials, with a large experimental effort being invested to unveil their electronic correlation effects/properties. Some compounds, such as the transition metal dichalcogenides, exhibit complex phase diagrams, with charge-density wave (CDW), superconductivity, and topological phases, that are associated with strong electron-phonon (e-ph) interactions. Interestingly, even for cuprates, materials well-known by their strong electron-electron (e-e) interactions, recent findings provide evidence for non-neglectable effects of the e-ph coupling inside the doped region. These findings have raised issues about the relevance of the e-ph coupling for correlated materials, rather than just e-e interactions. Indeed, understanding how to control and manipulate these many-body states remains a challenge for theoretical and experimental physicists, and it is the bottleneck for eventual applications on semiconducting devices.

As a step towards this, Dr. Costa (CM-SISSA), Prof. Sorella (CM-SISSA), and collaborators investigated fundamental properties of the e-e and e-ph interactions by analyzing an effective Hamiltonian. They developed state-of-the-art quantum Monte Carlo methods to study the long-range ordering of the Hubbard-Holstein model in the square lattice, at half-filling. With this, they were able to analyze the competition and interplay between antiferromagnetism (AFM) and CDW, establishing its very rich phase diagram. Interestingly, in the region between AFM and CDW phases, they have found an enhancement of superconducting pairing correlations, favoring (nonlocal) s-wave pairs. Besides correcting past inconsistencies in the literature, namely the emergence of CDW in the pure Holstein model, this study provides new insights about the nature of the competition between CDW, superconductivity, and AFM, which is relevant to further understand the properties of correlated materials.

S.S. and N.C.C are grateful to SISSA for the financial support, and acknowledge PRACE for awarding them access to Marconi at CINECA, Italy (PRACE-2019204934).

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Dated: May 13, 2020