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arXiv:0809.4426 · Journal of Physics Condensed Matter

Ground-state properties of the two-site Hubbard–Holstein model: an exact solution

Yuyu Zhang, Tao Liu, Qing‐Hu Chen, Xiaoguang Wang, Ke-Lin Wang

Published Sep 23, 2009• 7 citations
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Abstract

We study the two-site Hubbard-Holstein model by using an extended phonon coherent state. For the nontrivial singlet bipolarons, the double occupancy probability, the fidelity and the entanglement entropy are calculated to characterize the ground-state properties in both two-site and single-site bipolaron-dominated regimes. We use the localized minimum of the fidelity to define a crossover and plot the bipolaron phase diagram, which separates the large and small entanglement region. Furthermore, the relation between the bipolaron entanglement and the correlation functions demonstrates that the large entanglement corresponds to the large magnitude of lattice deformations induced by electrons.

DOI
10.1088/0953-8984/21/41/415601

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We present a diagrammatic Monte Carlo study of the properties of the Hubbard-Holstein bipolaron on a two-dimensional square lattice. With a small Coulomb repulsion UUU and with increasing electron-phonon interaction, and when reaching a value about two times smaller than the one corresponding to the transition of light polaron to heavy polaron, the system suffers a sharp transition from a state formed by two weakly bound light polarons to a heavy, strongly bound on-site bipolaron. Aside from this rather conventional bipolaron a new bipolaron state is found for large UUU at intermediate and large electron-phonon coupling, corresponding to two polarons bound on nearest-neighbor sites. We discuss both the properties of the different bipolaron states and the transition from one state to another. We present a phase diagram in parameter space defined by the electron-phonon coupling and UUU. Our numerical method does not use any artificial approximation and can be easily modified to other bipolaron models with longer range electron-phonon and∕or electron-electron interaction.
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