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Study of supersolidity in the two-dimensional Hubbard–Holstein model

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Abstract

We derive an effective Hamiltonian for the two-dimensional Hubbard–Holstein model in the regimes of strong electron–electron and strong electron–phonon interactions by using a nonperturbative approach. In the parameter region where the system manifests the existence of a correlated singlet phase, the effective Hamiltonian transforms to a t1 − V 1 − V 2 − V 3 Hamiltonian for hard-core-bosons on a checkerboard lattice. We employ quantum Monte Carlo simulations, involving stochastic-series-expansion technique, to obtain the ground state phase diagram. At filling 1∕8, as the strength of off-site repulsion increases, the system undergoes a first-order transition from a superfluid to a diagonal striped solid with ordering wavevector \(\vec{Q}\) = (π∕4, 3π∕4) or (π∕4, 5π∕4). Unlike the one-dimensional situation, our results in the two-dimensional case reveal a supersolid phase (corresponding to the diagonal striped solid) around filling 1∕8 and at large off-site repulsions. Furthermore, for small off-site repulsions, we witness a valence bond solid at one-fourth filling and tiny phase-separated regions at slightly higher fillings.

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Authors and Affiliations

  1. CMP Division, Saha Institute of Nuclear Physics, HBNI, Kolkata, India

    Amrita Ghosh & Sudhakar Yarlagadda

  2. Theoretical Physics Department, Indian Association for the Cultivation of Science, Kolkata, India

    Satyaki Kar

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  1. Amrita Ghosh
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Correspondence to Sudhakar Yarlagadda.

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Contribution to the Topical Issue “Coexistence of Long-Range Orders in Low-dimensional Systems”, edited by Sudhakar Yarlagadda and Peter B. Littlewood.

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Ghosh, A., Kar, S. & Yarlagadda, S. Study of supersolidity in the two-dimensional Hubbard–Holstein model. Eur. Phys. J. B 91, 205 (2018). https://doi.org/10.1140/epjb/e2018-90350-y

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