Related papers: Chern numbers in quantum graphs
The Chern number is often used to distinguish between different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline…
We study the properties of the quantum states in the one-dimensional system with a shifted periodic potential in both the discrete model and the continuous model. With open boundary conditions, the edge states appear in the energy gaps…
We study Chern numbers to characterize the ground state of strongly interacting systems on a lattice. This method allows us to perform a numerical characterization of bosonic fractional quantum Hall (FQH) states on a lattice where…
The spectral theory of quantum graphs is related via an exact trace formula with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The latter is a degenerate spectrum, and understanding its structure (i.e.,finding out…
Chern numbers are gaining traction as they characterize topological phases in various physical systems. However, the resilience of the system topology to external perturbations makes it challenging to experimentally investigate transitions…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
Topological invariants, such as the Chern number, characterise topological phases of matter. Here we provide a method to detect Chern numbers in systems with two distinct species of fermion, such as spins, orbitals or several atomic states.…
Quasi-periodic quantum spin chains were recently found to support many topological phases in the finite magnetization sectors. They can simulate strong topological phases from class A in arbitrary dimension that are characterized by first…
We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped"…
Topological Chern indices are related to the number of rotational states in each molecular vibrational band. Modification of the indices is associated to the appearance of ``band degeneracies'', and exchange of rotational states between two…
The geometrically frustrated Kitaev magnets are demonstrated to be fertile playgrounds that allow for the occurrence of exotic phenomena, including topological phases and the thermal Hall effect. Notwithstanding the established consensus…
In 2D semiconductors and insulators, the Chern number of the valence band Bloch state is an important quantity that has been linked to various material properties, such as the topological order. We elaborate that the opacity of 2D materials…
For various two dimensional lattices such as honeycomb, kagome, and square-octagon, gauge conventions (string gauge) realizing minimum magnetic fluxes that are consistent with the lattice periodicity are explicitly given. Then many-body…
We classify the topology of bands defined by the energy states of quantum systems with scale separation between slow and fast degrees of freedom, invariant under fermionic time reversal. Classical phase space transforms differently from…
Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from…
Topological invariants are global properties of the ground-state wave function, typically defined as winding numbers in reciprocal space. Over the years, a number of topological markers in real space have been introduced, allowing to map…
We study the relation between Chern numbers and Quantum Phase Transitions (QPT) in the XY spin-chain model. By coupling the spin chain to a single spin, it is possible to study topological invariants associated to the coupling Hamiltonian.…
Topological quantum phase transitions in superconductivity are discussed on two dimensional lattices. The main focus is on the Chern number for superconducting states. Each superconductivity is characterized by the Chern number, and the…
Chern number is a crucial invariant for characterizing topological feature of two-dimensional quantum systems. Real-space Chern number allows us to extract topological properties of systems without involving translational symmetry, and…
Topological invariants such as Chern classes are by now a standard way to classify topological phases. Introducing and varying parameters in such systems leads to phase diagrams, where the Chern classes may jump when crossing a critical…