Related papers: Topological Hamiltonian as an Exact Tool for Topol…
We discuss a topological classification of insulators and superconductors in the presence of both (non-spatial) discrete symmetries in the Altland-Zirnbauer classification and spatial reflection symmetry in any spatial dimensions. By using…
Owing to the presence of exceptional points (EPs), non-Hermitian (NH) systems can display intriguing topological phenomena without Hermitian analogs. However, experimental characterizations of exceptional topological invariants have been…
Defects which appear in heterostructure junctions involving topological insulators are sources of gapless modes governing the low energy properties of the systems, as recently elucidated by Teo and Kane [Physical Review B82, 115120 (2010)].…
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…
The spectral localizer is a predictive framework for the computation of topological invariants of natural and artificial materials. Here, three crucial improvements on the criterion for the validity of the framework are reported: first,…
Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local-global correspondence between the…
In this work, we present a new diagrammatic method for computing the effective Hamiltonian of driven nonlinear oscillators. At the heart of our method is a self-consistent perturbation expansion developed in phase space, which establishes a…
For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each…
We present a proposal for the realization of entanglement Hamiltonians in one-dimensional critical spin systems with strongly interacting cold atoms. Our approach is based on the notion that the entanglement spectrum of such systems can be…
The aim of this series of two papers is to discuss topological invariants for interacting topological insulators (TIs). In the first paper (I), we provide a paradigm of efficient numerical evaluation scheme for topological invariants, in…
The topological invariants of gapped time reversal invariant lattice superconductors are studied by mapping the superconducting mean field Hamiltonian to a Bloch Hamiltonian. There is a single $Z_2 $ invariant in two dimensions and four…
The three-dimensional topological insulator \ce{Bi2Te3} differs from other topological insulators in the \ce{Bi2Se3} family in that the effective Hamiltonian of its surface states on a flat semi-infinite slab requires the addition of a…
Interaction effects have been a subject of contemporary interest in topological phases of matter. But in the presence of interactions, the accurate determination of topological invariants in their general form is difficult due to their…
Topological insulators are characterized by insulating bulk and conducting surface, the latter is a necessity consequence of the nontrivial topology of the wavefunctions forming the valence band. This chapter gives a historical overview of…
Recent studies have extended the notion of band topology to nonlinear systems by defining nonlinear counterparts of eigenvalue problems. They have found the nonlinearity-induced topological transition, while it has required complicated…
We consider topological invariants describing semimetal (gapless) and insulating (gapped) states of the quantum vacuum of Standard Model and possible quantum phase transitions between these states.
The topological properties of materials are, until now, associated with the features of their crystalline structure, although translational symmetry is not an explicit requirement of the topological phases. Recent studies of hopping models…
Protected by the chiral symmetry, three dimensional chiral topological insulators are characterized by an integer-valued topological invariant. How this invariant could emerge in physical observables is an important question. Here we show…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
We study Hamiltonian flows in a real separable Hilbert space endowed with a symplectic structure. Measures on the Hilbert space that are invariant with respect to the flows of completely integrable Hamiltonian systems are investigated.…