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Register a new userWavefunction Vortex Attachment via Matrix Products: Application to Atomic Fermi Gases in Flat Spin-Orbit Bands
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V.W. Scarola
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Variational wavefunctions that introduce zeros (vortices) to screen repulsive interactions are typically difficult to verify in unbiased microscopic calculations. An approach is constructed to insert vortices into ansatz wavefunctions using a matrix product representation. This approach opens the door to validation of a broad class of Jastrow-based wavefunctions. The formalism is applied to a model motivated by experiments on ultracold atomic gases in the presence of synthetic spin-orbit coupling. Validated wavefunctions show that vortices in atomic Fermi gases with flat Rashba spin-orbit bands cluster near the system center and should therefore be directly visible in time-of-flight imaging.
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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. We find that the energy as a function of the magnetic flux threading the ring has a half-flux quantum $Phi_0/2 = hc/(2e)$ period, indicating that only bound pairs of particles with charge $2e$ are propagating, while single quasiparticles with charge $e$ remain localized. We show analytically in one dimension 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 we construct an extensive number of exact conserved quantities for the one dimensional lattice models. These conserved quantities are associated to the occupation of localized single quasiparticle states. Our results imply that in lattice models with flat bands preformed pairs dominate transport even above the critical temperature of the transition to a superfluid state.
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