Re-investigation of the ground state phases of the one-dimensional half filled Hubbard-Holstein model

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The interplay between electronic degrees of freedom and lattice vibrations is at the heart of the description of many important physical phenomena but also observed in many real materials.

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The paradigmatic model in order to study such interactions between electronic and phononic degrees of freedom is the one dimensional Hubbard Holstein model.

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This extends the usual single band Hubbard model by coupling to harmonic oscillator like nuclei.

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In particular, the intermediate regime where the strength of both interactions becomes comparable is difficult to access, both analytically and numerically, and was therefore subject to controversial discussions.

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Recent advances in tensor network techniques allow us to access the properties of theses systems in a highly controlled fashion even though the individual bosonic Hilbert spaces are infinitely dimensional and violate particle number conservation symmetry.

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Doing so, we were able to compute a phase diagram with a high degree of accuracy and not suffering from both small systems sizes and local Hilbert spaces, in contrast to prior investigations.

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Explicitly, we looked at the influence of the phononic degrees of freedom on the anti ferromagnetic and Peierls insulating states and dealt with the nature of the intermediate state.

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Finally, we observed an unusual behaviour with the occurrence of a non-integer central charge.

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