Related papers: Non-Abelian hyperbolic band theory from supercells
Periodic lattices in hyperbolic space are characterized by symmetries beyond Euclidean crystallographic groups, offering a new platform for classical and quantum waves, demonstrating great potentials for a new class of topological…
The hyperbolic lattice (HBL) has emerged as a compelling platform for exploring matter in non-Euclidean space. Among its notable features, the breakdown of the conventional Bloch theorem stands out, prompting a reexamination of band theory,…
Hyperbolic lattices are a new form of synthetic quantum matter in which particles effectively hop on a discrete tessellation of 2D hyperbolic space, a non-Euclidean space of uniform negative curvature. To describe the single-particle…
Real-valued band structures are foundational to analyzing periodic systems within the Hermitian description and have been experimentally well-established over recent decades. In contrast, non-Hermitian systems exhibit complex band…
We extend the notion of topologically protected semi-metallic band crossings to hyperbolic lattices in a negatively curved plane. Because of their distinct translation group structure, such lattices are associated with a high-dimensional…
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…
Hyperbolic lattices underlie a new form of quantum matter with potential applications to quantum computing and simulation and which, to date, have been engineered artificially. A corresponding hyperbolic band theory has emerged, extending…
The notions of Bloch wave, crystal momentum, and energy bands are commonly regarded as unique features of crystalline materials with commutative translation symmetries. Motivated by the recent realization of hyperbolic lattices in circuit…
Topological band theory establishes a standardized framework for classifying different types of topological matters. Recent investigations have shown that hyperbolic lattices in non-Euclidean space can also be characterized by hyperbolic…
Hyperbolic lattices are starting to be explored in search of novel phases of matter. At the same time, non-Hermitian physics has come to the forefront in photonic, optical, phononic, and condensed matter systems. In this work, we introduce…
We explore algebras associated with the hyperbolic band theory under a magnetic field for the first time. We define the magnetic Fuchsian group associated with a higher genus Riemann surface. By imposing the magnetic boundary conditions for…
In spatially periodic Hermitian systems, such as electronic systems in crystals, the band structure is described by the band theory in terms of the Bloch wave functions, which reproduce energy levels for large systems with open boundaries.…
Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence…
Non-Abelian physics, originating from noncommutative sequences of operations, unveils novel topological degrees of freedom for advancing band theory and quantum computation. In photonics, significant efforts have been devoted to developing…
Wavefunction effects in uncorrelated systems are characterized by the Berry curvature and quantum metric. Beyond those, we propose gauge-independent tensors describing Bloch wavefunction effects on local interaction between correlated…
Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the…
Braiding has attracted significant attention in physics because of its important role in describing the fundamental exchange of particles. Infusing the braiding with topological protection will make it robust against imperfections and…
We study topological properties of one-dimensional nonlinear bichromatic superlattices and unveil the effect of nonlinearity on topological states. We find the existence of nontrivial edge solitions, which distribute on the boundaries of…
Recently, hyperbolic lattices that tile the negatively curved hyperbolic plane emerged as a new paradigm of synthetic matter, and their energy levels were characterized by a band structure in a four- (or higher-)dimensional momentum space.…
One of the most pronounced non-Hermitian phenomena is the non-Hermitian skin effect, which refers to the exponential localization of bulk eigenstates near the boundaries of non-Hermitian systems. Whereas non-Bloch band theory has been…