Phase diagram and pair Tomonaga-Luttinger liquid in a Bose-Hubbard model with flat bands

Takayoshi, Shintaro; Katsura, Hosho; Watanabe, Noriaki; Aoki, Hideo

doi:10.1103/physreva.88.063613

Cited by 87 publications

(96 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By contrast, our result shows that it is possible to find repulsively bound pairs, in the medium, even when the particles are completely forbidden from overlapping. We note also that liquids of bound pairs have been found theoretically on the flat-band Creutz ladder in the weak-coupling limit [19,28].…”

Section: Introductionmentioning

confidence: 95%

Low-energy behavior of strongly interacting bosons on a flat-band lattice above the critical filling factor

et al. 2015

View full text Add to dashboard Cite

Bosons interacting repulsively on a lattice with a flat lowest band energy dispersion may, at sufficiently small filling factors, enter into a Wigner-crystal-like phase. This phase is a consequence of the dispersionless nature of the system, which in turn implies the occurrence of single-particle localized eigenstates. We investigate one of these systems-the sawtooth lattice-filled with strongly repulsive bosons at filling factors infinitesimally above the critical point where the crystal phase is no longer the ground state. We find, in the hard-core limit, that the crystal retains its structure in all but one of its cells, where it is broken. The broken cell corresponds to an exotic kind of repulsively bound state, which becomes delocalized. We investigate the excitation spectrum of the system analytically and find that the bound state behaves as a single particle hopping on an effective lattice with reduced periodicity, and is therefore gapless. Thus, the addition of a single particle to a flat-band system at critical filling is found to be enough to make kinetic behavior manifest.

show abstract

Section: Introductionmentioning

confidence: 95%

Low-energy behavior of strongly interacting bosons on a flat-band lattice above the critical filling factor

et al. 2015

View full text Add to dashboard Cite

show abstract

“…A prime example is the fractional quantum Hall effect [1]. Beyond the physics in a strong magnetic field, flat or nearly flat bands are a relatively common occurrence in lattice Hamiltonians where they can be realized by engineering suitable hopping matrix elements [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Given the vanishing group velocity, one could expect an electronic flat band system to be a particularly bad conductor.…”

Section: Introductionmentioning

confidence: 99%

Effective theory and emergent SU(2) symmetry in the flat bands of attractive Hubbard models

et al. 2016

View full text Add to dashboard Cite

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. Nevertheless, 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 the 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, if a simple uniform pairing condition on the single-particle states is satisfied, 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 W 2 between the Drude weight D and the winding number W, which guarantees ballistic transport for topologically nontrivial flat bands in one dimension.

show abstract

“…However, interactions and disorder lead to a reconstruction of the ground state whose properties are often hard to predict. Bands that are nearly flat and/or feature a nontrivial topological invariant, similar to Landau levels producing the quantum Hall effects [2][3][4], have been considered in recent theoretical works [5][6][7][8][9][10][11][12] and can be realized in ultracold gas experiments [13][14][15]. Flat-band ferromagnetism has been studied first by Lieb [16] and, subsequently, by Tasaki and Mielke [17][18][19][20].…”

mentioning

confidence: 99%

Geometric Origin of Superfluidity in the Lieb-Lattice Flat Band

et al. 2016

View full text Add to dashboard Cite

The ground state and transport properties of the Lieb lattice flat band in the presence of an attractive Hubbard interaction are considered. It is shown that the superfluid weight can be large even for an isolated and strictly flat band. Moreover the superfluid weight is proportional to the interaction strength and to the quantum metric, a band structure quantity derived solely from the flat-band Bloch functions. These predictions are amenable to verification with ultracold gases and may explain the anomalous behaviour of the superfluid weight of high-Tc superconductors.

show abstract

Phase diagram and pair Tomonaga-Luttinger liquid in a Bose-Hubbard model with flat bands

Cited by 87 publications

References 33 publications

Low-energy behavior of strongly interacting bosons on a flat-band lattice above the critical filling factor

Low-energy behavior of strongly interacting bosons on a flat-band lattice above the critical filling factor

Effective theory and emergent SU(2) symmetry in the flat bands of attractive Hubbard models

Geometric Origin of Superfluidity in the Lieb-Lattice Flat Band

Contact Info

Product

Resources

About