相关论文: Tile Hamiltonian for Decagonal AlCoCu
A cascade of phase transitions from square to hexagonal lattice is studied in 2D system of particles interacting via core-softened potential. Due to the presence of two length-scales of repulsion, different local configurations with four,…
Higher-order topological crystalline phases in low-dimensional interacting quantum systems represent a challenging and largely unexplored research topic. Here, we derive a Hamiltonian describing fermions interacting through correlated…
We propose a means to realize two-dimensional quasiperiodic structures by trapping atoms in an optical potential. The structures have eight-fold symmetry and are closely related to the well-known quasiperiodic octagonal (Ammann-Beenker)…
We find exact solutions to the Hamiltonian of a 16-site spin-1/2 pyrochlore crystal with nearest neighbour exchange interactions. The methods of group theory (symmetry) are used to completely block-diagonalize the Hamiltonian, yielding…
Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for quantum many-body states of matter that previously had not been accessible. Here we introduce a symmetry-based method of…
We consider interacting paraparticle chains with a constant $R$-matrix where the Hamiltonian sums over the internal degrees (flavors) of the paraparticles. For such flavor-blind Hamiltonians we show a general factorization of the Hilbert…
High-order topological insulators (HOTIs), as generalized from topological crystalline insulators (TCIs), are characterized with lower-dimensional metallic boundary states protected by spatial symmetries of a crystal, whose theoretical…
Traditional topological materials belong to different Altland-Zirnbauer symmetry classes (AZSCs) depending on their non-spatial symmetries. Here we introduce the notion of hybrid symmetry class topological insulators (HSCTIs): A fusion of…
Transition metal dichalcogenides XTe$_{2}$ (X=Mo,W) have been shown to be second-order topological insulators based on first-principles calculations, while topological hinge states have been shown to emerge based on the associated…
The strict geometric rules that define aperiodic tilings lead to the unique spectral and transport properties of quasicrystals, but also limit our ability to design them. In this Letter, we explore a novel example of a continuously tunable…
Superconductivity in graphene-based systems has recently attracted much attention, as either intrinsic behavior or induced by proximity to a superconductor may lead to interesting topological phases and symmetries of the pairing function. A…
Square-root higher-order topological insulators (HOTIs) are recently discovered new topological phases, with intriguing topological properties inherited from a parent lattice Hamiltonian. Different from conventional HOTIs, the square-root…
The non-interacting band structure of spinless fermions in a two-dimensional ($d=2$) $p$-band honeycomb lattice exhibits two quadratic band touching points (QBTPs), which lie at the Fermi levels of filling $\nu=1/4$ and its particle-hole…
Stimulated by recent works highlighting the indispensable role of Coulomb interactions in the formation of helical chains and chiral electronic order in the elemental chalcogens, we explore the p-orbital Hubbard model on a one-dimensional…
A longstanding open problem asks for an aperiodic monotile, also known as an "einstein": a shape that admits tilings of the plane, but never periodic tilings. We answer this problem for topological disk tiles by exhibiting a continuum of…
In a recent Letter we proposed a means to realize a quasicrystal with eight-fold symmetry by trapping particles in an optical potential created by four lasers. The quasicrystals obtained in this way, which are closely related to the…
Strongly interacting fermionic atoms on optical lattices are studied through a Hubbard-like model Hamiltonian, in which tunneling rates of atoms and molecules between neighboring sites are assumed to be different. In the limit of large…
We describe a way to obtain a two-dimensional quasiperiodic tiling with eight-fold symmetry using cold atoms. A series of such optical tilings, related by scale transformations, is obtained for a series of specific values of the chemical…
Square-root topological states are new topological phases, whose topological property is inherited from the square of the Hamiltonian. We realize the first-order and second-order square-root topological insulators in phononic crystals, by…
Composite Higgs models with anarchic partial compositeness require a scale of new physics ${\cal O}(10-100)$ TeV, with the bounds being dominated by the dipole moments and $\epsilon_K$. The presence of anarchic bilinear interactions can…