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arXiv:1505.00578 · Journal of Magnetism and Magnetic Materials

Magnetic phase diagram of the Hubbard model in the Lieb lattice

José Daniel Gouveia, R. G. Dias

Published Feb 7, 2015• 20 citations
arXivHTMLPDF
DOI
10.1016/j.jmmm.2015.02.005

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We investigate the magnetic orders and excitations in a half-filled Hubbard model that continuously interpolates between the Lieb and kagome lattices. Using the self-consistent Hartree-Fock approximation combined with the Bethe-Salpeter equation in the random phase approximation, we map the U − t ′ phase diagram of the Lieb-kagome lattices and compute real-frequency transverse spin susceptibilities, i.e., the magnon spectra. Dynamical mean-field theory and exact diagonalization are used as complementary checks of static magnetic phases. In particular, besides gapless Goldstone magnons, the symmetry-broken ferrimagnetic and antiferromagnetic phases also exhibit gapped Higgs magnon bands, which originate from amplitude fluctuations in the order parameter characterizing spontaneous symmetry breaking.
We investigate interacting bosons on a two-dimensional Lieb lattice, taking into account kinetic tunneling terms between the nearest-neighboring and next-nearest-neighboring sites. In the frame of a time-dependent variational Gutzwiller method, ground states of the Bose–Hubbard model are accessible site by site. As a consequence, we figure out an exotic type of supersolid phase which particularly features a dual construction, but in the absence of interactions among different lattice sites. This dual supersolid state could be further supported by solving the Bose–Hubbard model via an exact diagonalization method, and feasibly generalized to a limiting case of hardcore bosons. We also map out the phase diagram with the help of the time-dependent variational Gutzwiller method. And it manifests that the regime of dual supersolid state is dominant. • The Bose–Hubbard model on the Lieb lattice is studied. • We identify the dual supersolid without off-site interaction. • We map out the phase diagram of the bosonic Lieb lattice.