Kazuto Noda

Flat-band ferromagnetism in the multilayer Lieb optical lattice

We theoretically study magnetic properties of two-component cold fermions in half-filled multilayer Lieb optical lattices, i.e., two, three, and several layers, using the dynamical mean-field theory. We clarify that the magnetic properties of this system become quite different depending on whether the number of layers is odd or even. In odd-number-th layers in an odd-number-layer system, finite magnetization emerges even with an infinitesimal interaction. This is a striking feature of the flatband ferromagnetic state in multilayer systems as a consequence of the Lieb theorem. In contrast, in even-number layers, magnetization develops from zero on a finite interaction. These different magnetic behaviours are triggered by the flat bands in the local density of states and become identical in the limit of the infinite-layer (i.e., three-dimensional) system. We also address how interlayer hopping affects the magnetization process. Further, we point out that layer magnetization, which is a population imbalance between up and down atoms on a layer, can be employed to detect the emergence of the flat-band ferromagnetic state without addressing sublattice magnetization.

Effects of Disorder on Superfluidity in the Attractive Hubbard Model

We study the effects of disorder on an \(s\)-wave superfluid in the attractive Hubbard model using statistical dynamical mean-field theory, which enables us to treat both the correlation effects and the spatial nonuniformity due to disorder in the same framework. The distribution functions of the local density of states and the superfluid order parameter are obtained. From the geometrical average of these quantities, which characterizes the order parameters in disordered systems, we determine the ground-state phase diagram of the attractive Hubbard model with disorder at half-filling and zero temperature. We discuss the superfluid-localization transition and the crossover behavior within the localized phase.

Magnetism in the three-dimensional layered Lieb lattice: Enhanced transition temperature via flat-band and Van Hove singularities

We describe the enhanced magnetic transition temperatures

P artial Kondo screening in a geometrically frustrated heavy electron system

T_c

Many-body effects in a Bose-Fermi mixture

of two-component fermions in three-dimensional layered Lieb lattices, which are created in cold atom experiments. We determine the phase diagram at half-filling using the dynamical mean-field theory. The dominant mechanism of enhanced

Quantum phases of Bose–Fermi mixtures in optical lattices

T_c

Magnetically ordered state of cold fermions on a decorated square lattice

gradually changes from the (delta-functional) flat-band to the (logarithmic) Van Hove singularity as the interlayer hopping increases. We elucidate that the interaction induces an effective flat-band singularity from a dispersive flat (or narrow) band. We offer a general analytical framework for investigating the singularity effects, where a singularity is treated as one parameter in the density of states. This framework provides a unified description of the singularity-induced phase transitions, such as magnetism and superconductivity, where the weight of the singularity characterizes physical quantities. This treatment of the flat-band provides the transition temperature and magnetization as a universal form (i.e., including the Lambert function). We also elucidate a specific feature of the magnetic crossover in magnetization at finite temperatures.

Ferromagnetism of cold fermions loaded into a decorated square lattice

We investigate a triangular Kondo lattice model by the dynamical mean-field theory combined with the numerical renormalization group. We particularly focus on a partial Kondo screening order with commensurate filling n = 2.0 on a three-site unit cell. It is demonstrated that two types of metal-insulator transition occur in the presence of this order. We also clarify that these transitions are Lifshitz transitions of first and second order.

Resistivity crossover in the power-law Kondo systems

We investigate many-body effects on a mixture of interacting bosons and fermions loaded in an optical lattice using a generalized dynamical mean field theory combined with the numerical renormalization group. We show that strong correlation effects emerge in the presence of bosonic superfluidity, leading to a renormalized peak structure near the Fermi level in the density of states for fermions. Remarkably, this kind of strong renormalization appears not only in the metallic phase but also in the insulating phases of fermions such as in the empty/filled band limit. A systematic analysis of the relation between the quasiparticle weight and the strength of superfluidity reveals that the renormalization effect is indeed caused by the boson degrees of freedom. It is found that such renormalization is also relevant to a supersolid phase consisting of a density wave ordering of fermions accompanied by bosonic superfluidity. This sheds light on the origin of the peak structure in the supersolid phase.

BCS superconducting transitions in lattice fermions

We consider a mixture of interacting bosons and fermions in optical lattices described by the Bose–Fermi Hubbard Hamiltonian. To treat bosonic degrees of freedom, we use a generalized dynamical mean field theory (GDMFT). By combining the GDMFT with the numerical renormalization group method, we revisit the zero-temperature phase diagram with particular emphasis on many-body effects in a supersolid state and discuss the origin of an anomalous peak structure emerging in the density of states for fermions.