Related papers: Approximations of interface topological invariants
The time evolution of topological systems is an active area of interest due to their expected applications in fault-tolerant quantum computing. Here, we analyze the dynamics of a noninteracting spinless fermion chain in its topological…
Two-dimensional topological insulators, and in particular quantum Hall states, are characterized by an insulating bulk and a conducting edge. Fractional states may host both downstream (dictated by the magnetic field) and upstream…
The paper deals with the problem of the existence of a normal form for a nearly-integrable real-analytic Hamiltonian with aperiodically time-dependent perturbation decaying (slowly) in time. In particular, in the case of an isochronous…
In this essay, we first sketch the development of ideas on the extraordinary dynamics of integrable classical nonlinear and quantum many body Hamiltonians. In particular, we comment on the state of mathematical techniques available for…
The unambiguous detection of the band topology for topological nodal systems remains an urgent problem in this field. Usually in experiments this relies on the detection for the topological edge modes, which may requires the high demands…
We present a method for deriving bulk and edge invariants for interacting, many-body localized Floquet systems in two spatial dimensions. This method is based on a general mathematical object which we call a flow. As an application of our…
We introduce an effective edge network theory to characterize the boundary topology of coupled edge states generated from various types of topological insulators. Two examples studied are a two-dimensional second-order topological insulator…
The discovery of the quantised Hall effect, and its subsequent topological explanation, demonstrated the important role topology can play in determining the properties of quantum systems. This realisation led to the development of…
In modern condensed matter theory, phases of electronic matter--such as metals and insulators-are fundamentally distinguished by the presence or absence of charge-carrying quasiparticles or excitations near the Fermi surface at low…
In two dimensions, interacting Floquet topological phases may arise even in the absence of any protecting symmetry, exhibiting chiral edge transport that is robust to local perturbations. We explore a similar class of Floquet topological…
Recent explorations of quantized solitons transport in optical waveguides have thrust nonlinear topological pumping into the spotlight. In this work, we introduce a unified topological invariant applicable across both weakly and strongly…
We study a one-dimensional system that includes both a commensurate off-diagonal modulation of the hopping amplitude and an incommensurate, slowly varying diagonal on-site modulation. By using asymptotic heuristic arguments, we identify…
We investigate the quantum dynamics of wave packets in a class of decorated lattices, both quasiperiodic and random, where a nominal quasi-one dimensionality is introduced at local levels, bringing in a deterministic or even random…
We establish a quantitative bulk-boundary correspondence in interacting topological insulators by relating many-body topological invariants to characteristic degeneracy structures in the entanglement spectrum. Focusing on generalized…
We propose a new example of discrete holography that provides a new step towards establishing the AdS/CFT duality for discrete spaces. A class of boundary Hamiltonians is obtained in a natural way from regular tilings of the hyperbolic…
We study the modular Hamiltonians of an interval for the massless Dirac fermion on the half-line. The most general boundary conditions ensuring the global energy conservation lead to consider two phases, where either the vector or the axial…
Most natural and artificial materials have crystalline structures from which abundant topological phases emerge [1-6]. The bulk-edge correspondence, widely-adopted in experiments to determine the band topology from edge properties, however,…
The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…
In this chapter we review our work on the theory of quantum transport in topological insulator nanowires. We discuss both normal state properties and superconducting proximity effects, including the effects of magnetic fields and disorder.…
We study transport properties of the helical edge states of two-dimensional integer and fractional topological insulators via double constrictions. Such constrictions couple the upper and lower edges of the sample, and can be made and tuned…