Browsing by Author "Huber, Sebastian D."

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Effective theory and emergent SU(2) symmetry in the flat bands of attractive Hubbard models
(2016-12-30) Tovmasyan, Murad; Peotta, Sebastiano; Törmä, Päivi; Huber, Sebastian D.
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
In a partially filled flat Bloch band electrons do not have a well defined Fermi surface and hence the low-energy theory is not a Fermi liquid. Neverethless, under the influence of an attractive interaction, a superconductor well described by the Bardeen-Cooper-Schrieffer (BCS) wave function can arise. Here we study the low-energy effective Hamiltonian of a generic Hubbard model with a flat band. We obtain an effective Hamiltonian for the flat band physics by eliminating higher lying bands via perturbative Schrieffer-Wolff transformation. At first order in the interaction energy we recover the usual procedure of projecting the interaction term onto the flat band Wannier functions. We show that the BCS wave function is the exact ground state of the projected interaction Hamiltonian and that the compressibility is diverging as a consequence of an emergent SU(2) symmetry. This symmetry is broken by second order interband transitions resulting in a finite compressibility, which we illustrate for a one-dimensional ladder with two perfectly flat bands. These results motivate a further approximation leading to an effective ferromagnetic Heisenberg model. The gauge-invariant result for the superfluid weight of a flat band can be obtained from the ferromagnetic Heisenberg model only if the maximally localized Wannier functions in the Marzari-Vanderbilt sense are used. Finally, we prove an important inequality D≥W2 between the Drude weight D and the winding number W, which guarantees ballistic transport for topologically nontrivial flat bands in one dimension.
Preformed pairs in flat Bloch bands
(2018) Tovmasyan, Murad; Peotta, Sebastiano; Liang, Long; Törmä, Päivi; Huber, Sebastian D.
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
In a flat Bloch band, the kinetic energy is quenched and single particles cannot propagate since they are localized due to destructive interference. Whether this remains true in the presence of interactions is a challenging question because a flat dispersion usually leads to highly correlated ground states. Here we compute numerically the ground-state energy of lattice models with completely flat band structure in a ring geometry in the presence of an attractive Hubbard interaction. We find that the energy as a function of the magnetic flux threading the ring has a half-flux quantum Φ0/2=hc/(2e) period, indicating that only bound pairs of particles with charge 2e are propagating, while single quasiparticles with charge e remain localized. For some one-dimensional lattice models, we show analytically that in fact the whole many-body spectrum has the same periodicity. Our analytical arguments are valid for both bosons and fermions, for generic interactions respecting some symmetries of the lattice and at arbitrary temperatures. Moreover, for the same one-dimensional lattice models, we construct an extensive number of exact conserved quantities. These conserved quantities are associated to the occupation of localized single quasiparticle states and force the single-particle propagator to vanish beyond a finite range. Our results suggest that in lattice models with flat bands preformed pairs dominate transport even above the critical temperature of the transition to a superfluid state.