相关论文: Exact Topological Flat Bands from Continuum Landau…

We present the theory and experimental demonstration of a topological classification of finite tight binding Hamiltonians with chiral symmetry. Using the graph-theoretic notion of complete matchings, we show that many chiral tight binding…

We report the appearance of multiple numbers of completely flat band states in an extended Lieb lattice model in two dimensions with five atomic sites per unit cell. We also show that this edge-centered square lattice can host intriguing…

Flatbands play an important role in correlated quantum matter and have novel applications in photonic lattices. Synthetic magnetic fields and destructive interference in lattices are traditionally used to obtain flatbands. However, such…

Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two…

In this paper, we investigate solvable structures associated to Hamiltonian equations. For a completely integrable Hamiltonian system with $n$ degrees of freedom, we construct a canonical solvable structure consisting of $2n$ Hamiltonian…

Flat-band topologies and localizations in non-interacting systems are extensively studied in different quantum and classical-wave systems. Recently, the exploration on the novel physics of flat-band localizations and topologies in…

We introduce the concept of "quantum geometric nesting'' (QGN) to characterize the idealized ordering tendencies of certain flat-band systems implicit in the geometric structure of the flat-band subspace. Perfect QGN implies the existence…

We study the Hofstadter butterfly and Landau levels of the twisted bilayer graphene (TBG). We show that the nontrivial fragile topology of the lowest two bands near the charge neutral point makes their Hofstadter butterfly generically…

In this paper, we use elementary and simple ideas which are based on the significant applications of the power set ring to rebuild and study the patch topology on the prime spectrum from a completely different and new point of view.…

Materials that have zero-energy flat band states on the surface may show surface superconductivity. Here we report a theoretical observation that a Hamiltonian describing a thin slab of topological nodal line semimetal, has zero energy…

The topological classification of gapped band structures depends on the particular definition of topological equivalence. For translation-invariant systems, stable equivalence is defined by a lack of restrictions on the numbers of occupied…

In this paper we give the full microscopic derivation of the model Hamiltonian for the three dimensional topological insulators in the $Bi_2Se_3$ family of materials ($Bi_2Se_3$, $Bi_2Te_3$ and $Sb_2Te_3$). We first give a physical picture…

We study the entanglement Hamiltonian for the ground state of one-dimensional free fermions in the presence of an inhomogeneous chemical potential. In particular, we consider a lattice with a linear, as well as a continuum system with a…

Topological excitons are superpositions of electron-hole pair states, characterized by an envelope function with finite vorticity in momentum space. This vorticity is determined by the underlying topology of the electronic bands. We derive…

Conformal field theory has recently been applied to derive few-body Hamiltonians whose ground states are lattice versions of fractional quantum Hall states. The exact lattice models involve interactions over long distances, which is…

We propose the concept of `topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of topological Hamiltonian are significantly different from the physical energy spectra, but we show…

We revisit the problem of characterizing band topology in dynamically-stable quadratic bosonic Hamiltonians that do not conserve particle number. We show this problem can be rigorously addressed by a smooth and local adiabatic mapping…

Motivated by the recent experimental realizations of hyperbolic lattices in circuit quantum electrodynamics and in classical electric-circuit networks, we study flat bands and band-touching phenomena in such lattices. We analyze…

We study the continuum limit of the entanglement Hamiltonian of a sphere for the massless scalar field in its ground state by employing the lattice model defined through the discretisation of the radial direction. In two and three spatial…

We introduce a minimum tight-binding model with only three parameters extracted from graphene and untwisted bilayer graphene. This model reproduces quantitatively the electronic structure of not only these two systems and bulk graphite near…