Related papers: Fractional topology and multi-period re-quantizati…
Open quantum systems exhibit dynamics ranging from unitary evolution to irreversible dissipation. While the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) equation uniquely characterizes Markovian CPTP evolution, many physical platforms…
We study topological properties of phase transition points of one-dimensional topological quantum phase transitions by assigning winding numbers defined on closed circles around the gap closing points in the parameter space of momentum and…
Topological matter exhibits exotic properties yet phases characterized by large topological invariants are difficult to implement, despite rapid experimental progress. A promising route toward higher topological invariants is via engineered…
We report the findings of fractional topological states in one-dimensional periodically modulated quantum spin chains with up to third neighbor interactions. By exact numerical studies, we demonstrate the existence of topologically…
We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported in Phys. Rev. Lett. \textbf{106}, 240503 (2011) is detailed and extended to qudits of different dimensions.…
We consider the $ U(1) $ sigma model in the two dimensional space-time which is a field-theoretical model possessing a nontrivial topology. It is pointed out that its topological structure is characterized by the zero-mode and the winding…
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we study the continuous variable entanglement for a system consisting of two independent harmonic oscillators interacting with a…
A topological phase can be engineered in quantum physics from the Bloch sphere of a spin-1/2 showing an hedgehog structure as a result of a radial magnetic field. We elaborate on a relation between the formation of an entangled wavefunction…
The interplay between topology and nonlinearity represents a central challenge in modern physics. Here, we investigate this interplay by considering a synthetic Su-Schrieffer-Heeger lattice with all-to-all nonlocal interactions. We find…
We report the first realization of a fractional topological phase in a fully unitary, noninteracting discrete-time quantum walk implemented on finite cyclic graphs. Using a single-coin split-step cyclic quantum walk (SCSS-CQW), we uncover…
Floquet topological systems have been shown to exhibit features not commonly found in conventional topological systems such as topological phases characterized by arbitrarily large winding numbers. This is clearly highlighted in the quantum…
Non-Hermiticity is expected to add far more physical features to the already rich Floquet topological phases of matter. Nevertheless, a systematic approach to characterize non-Hermitian Floquet topological matter is still lacking. In this…
We study the mechanism of decay of a topological (winding-number) excitation due to finite-size effects in a two-dimensional valence-bond solid state, realized in an $S=1/2$ spin model ($J$-$Q$ model) and studied using projector Monte Carlo…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
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…
I review why and how physical states with fractional quantum numbers can occur, emphasizing basic mechanisms in simple contexts. The general mechanism of charge fractionalization is the passage from states created by local action of fields…
We study the topological characterization of the energy gaps in general two-dimensional quasiperiodic systems consisting of multiple periodicities, represented by twisted two-dimensional materials. We show that every single gap is uniquely…
The emergence of non equilibrium topological phases in low dimensional systems offers an interesting route for material properties engineering. We analyze the dynamical modulation of two coupled one-dimensional chains, described by the…
In quantum systems theory one of the fundamental problems boils down to: given an initial state, which final states can be reached by the dynamic system in question. Here we consider infinite dimensional open quantum dynamical systems…
We propose a two-spin quantum-mechanical model with applied magnetic fields acting on the Poincar\'e-Bloch sphere, to reveal a new class of topological energy bands with Chern number one half for each spin-1/2. The mechanism behind this…