相关论文: Flat-band full localization and symmetry-protected…

In this work, we construct an exact projector Hamiltonian with interactions, which is given by a sum of mutually commuting operators called stabilizers. The model is based on the recently studied Creutz-ladder of fermions, in which…

Being dispersionless, flat bands on periodic lattices are solely characterized by their macroscopically degenerate eigenstates: compact localized states (CLSs) in real space and Bloch states in reciprocal space. Based on this property, this…

We construct and characterize tight binding Hamiltonians which contain a completely flat topological band made of continuum lowest Landau level wavefunctions sampled on a lattice. We find an infinite family of such Hamiltonians, with simple…

Using the decorated domain wall procedure, we construct Finite Depth Local Unitaries (FDLUs) that realize Fermionic Symmetry-Protected Topological (SPT) phases. This results in explicit 'full' commuting projector Hamiltonians, where 'full'…

Certain disorder-free Hamiltonians can be non-ergodic due to a \emph{strong fragmentation} of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing the notion of `statistically localized integrals of…

Topological flat bands at the Fermi level offer a promising platform to study a variety of intriguing correlated phase of matter. Here we present band engineering in the twisted orbital-active bilayers with spin-orbit coupling. The symmetry…

In this letter, we report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen stringnet model. The full Hamiltonian in our…

Realizing topological flat bands with tailored single-particle Hilbert spaces is a critical step toward exploring many-body phases, such as those featuring anyonic excitations. One prominent example is the Kapit-Mueller model, a variant of…

We derive symmetry-based conditions for tight-binding Hamiltonians with flatbands to have compact localized eigenstates occupying a single unit cell. The conditions are based on unitary operators commuting with the Hamiltonian and…

The topological properties of the flat band states of a one-electron Hamiltonian that describes a chain of atoms with $s-p$ orbitals are explored. This model is mapped onto a Kitaev-Creutz type model, providing a useful framework to…

The existence of flat bands is generally thought to be physically possible only for dimensions larger than one. However, by exciting a system with different orthogonal states this condition can be reformulated. In this work, we demonstrate…

Exotic phases of matter emerge from the interplay between strong electron interactions and non-trivial topology. Owing to their lack of dispersion at the single-particle level, systems harboring flat bands are excellent testbeds for…

Flat bands (FB) are strictly dispersionless bands in the Bloch spectrum of a periodic lattice Hamiltonian, recently observed in a variety of photonic and dissipative condensate networks. FB Hamiltonians are finetuned networks, still lacking…

Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and…

Flat energy bands of model lattice Hamiltonians provide a key ingredient in designing dispersionless wave excitations and have become a versatile platform to study various aspects of interacting many-body systems. Their essential merit lies…

We develop a theory of edge states based on the Hermiticity of Hamiltonian operators for tight-binding models defined on lattices with boundaries. We describe Hamiltonians using shift operators which serve as differential operators in…

Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta $\Lambda$ in the Brillouin zone (BZ) with protected degeneracies at $\Lambda$. Commonly TIs are distinguished from trivial…

We describe fundamental equations which define the topological ground states in the lattice realization of the SU(2) BF phase. We introduce a new scalar Hamiltonian, based on recent works in quantum gravity and topological models, which is…

Existence of nontrivial topological phases in a tight binding Haldane-like model on the depleted Lieb lattice is reported. This two-band model is formulated by considering the nearest-neighbor, next-nearest-neighbor and…

In this work, we develop a systematic method of constructing flat-band models with and without band crossings. Our construction scheme utilizes the symmetry and spatial shape of a compact localized state (CLS) and also the singularity of…