Using density matrix renormalization group numerical calculations, we study the phase diagram of the half filled Bose-Hubbard system in the sawtooth lattice with strong frustration in the kinetic energy term. We focus in particular on values of the hopping terms which produce a flat band and show that, in the presence of contact and near neighbor repulsion, three phases exist: Mott insulator (MI), charge density wave (CDW), and the topological Haldane insulating (HI) phase which displays edge states and particle imbalance between the two ends of the system. We find that, even though the entanglement spectrum in the Haldane phase is not doubly degenerate, it is in excellent agreement with the entanglement spectrum of the Affleck-Kennedy-Lieb-Tasaki (AKLT) state built in the Wannier basis associated with the flat band. This emphasizes that the absence of degeneracy in the entanglement spectrum is not necessarily a signature of a nontopological phase, but rather that the (hidden) protecting symmetry involves nonlocal states. Finally, we also show that the HI phase is stable against small departure from flatness of the band but is destroyed for larger ones.Using density matrix renormalization group numerical calculations, we study the phase diagram of the half filled Bose-Hubbard system in the sawtooth lattice with strong frustration in the kinetic energy term. We focus in particular on values of the hopping terms which produce a flat band and show that, in the presence of contact and near neighbor repulsion, three phases exist: Mott insulator (MI), charge density wave (CDW), and the topological Haldane insulating (HI) phase which displays edge states and particle imbalance between the two ends of the system. We find that, even though the entanglement spectrum in the Haldane phase is not doubly degenerate, it is in excellent agreement with the entanglement spectrum of the Affleck-Kennedy-Lieb-Tasaki (AKLT) state built in the Wannier basis associated with the flat band. This emphasizes that the absence of degeneracy in the entanglement spectrum is not necessarily a signature of a nontopological phase, but rather that the (hidden) protecting symmetry involves nonlocal states. Finally, we also show that the HI phase is stable against small departure from flatness of the band but is destroyed for larger ones.

arXiv:1612.00550Physical review. B./Physical review. BApr 24, 201719 citations

Phase diagram of the Bilayer Bose Hubbard Model

Yanfei Tang, V. W. Scarola

Bulletin of the American Physical SocietyMar 3, 20150 citations

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

Shintaro Takayoshi, Hosho Katsura, Noriaki Watanabe +1 more

To explore superfluidity in flat-band systems, we consider a Bose-Hubbard model on a cross-linked ladder with $\ensuremath{\pi}$ flux, which has a flat band with a gap between the other band for noninteracting particles, where we study the effect of the on-site repulsion nonperturbatively. For low densities, we find exact degenerate ground states, each of which is a Wigner solid with nonoverlapping Wannier states on the flat band. At higher densities, the many-body system, when projected onto the lower flat band, can be mapped to a spin-chain model. This mapping enables us to reveal the existence of a Tomonaga-Luttinger liquid comprising pairs of bosons. Interestingly, the high- and low-density regions have an overlap, where the two phases coexist.To explore superfluidity in flat-band systems, we consider a Bose-Hubbard model on a cross-linked ladder with $\ensuremath{\pi}$ flux, which has a flat band with a gap between the other band for noninteracting particles, where we study the effect of the on-site repulsion nonperturbatively. For low densities, we find exact degenerate ground states, each of which is a Wigner solid with nonoverlapping Wannier states on the flat band. At higher densities, the many-body system, when projected onto the lower flat band, can be mapped to a spin-chain model. This mapping enables us to reveal the existence of a Tomonaga-Luttinger liquid comprising pairs of bosons. Interestingly, the high- and low-density regions have an overlap, where the two phases coexist.

arXiv:1309.6329Physical Review ADec 6, 201392 citations

Haldane Phase in Spin-1 Bosons with a Flat Band

Hong Wei Yang, Hayate Nakano, Hosho Katsura

We demonstrate that the Haldane phase can be realized with ultracold spin-1 atoms loaded on a lattice which has a flat band at the bottom of the band structure. The many-body ground state of the model Hamiltonian is exactly solvable in a special case, which turns out to serve as a representative of the Haldane phase. In this system, the Haldane phase is protected by $\mathbb{Z}_2 \times \mathbb{Z}_2$ spin rotation symmetry or time-reversal symmetry. Depending on several parameters, the Hamiltonian can either be in a gapped Haldane or a gapless critical phase. In a certain limit, the phase diagram is determined analytically by perturbation theory, while for general cases, the phase diagram is studied numerically by the variational uniform matrix product state (VUMPS) algorithm.We demonstrate that the Haldane phase can be realized with ultracold spin-1 atoms loaded on a lattice which has a flat band at the bottom of the band structure. The many-body ground state of the model Hamiltonian is exactly solvable in a special case, which turns out to serve as a representative of the Haldane phase. In this system, the Haldane phase is protected by $\mathbb{Z}_2 \times \mathbb{Z}_2$ spin rotation symmetry or time-reversal symmetry. Depending on several parameters, the Hamiltonian can either be in a gapped Haldane or a gapless critical phase. In a certain limit, the phase diagram is determined analytically by perturbation theory, while for general cases, the phase diagram is studied numerically by the variational uniform matrix product state (VUMPS) algorithm.

Mar 3, 20200 citations

\mathbb{Z}_2 \times \mathbb{Z}_2

spin rotation symmetry or time-reversal symmetry. Depending on several parameters, the Hamiltonian can either be in a gapped Haldane or a gapless critical phase. In a certain limit, the phase diagram is determined analytically by perturbation theory, while for general cases, the phase diagram is studied numerically by the variational uniform matrix product state (VUMPS) algorithm.