Related papers: Topological Superconductors and Category Theory
In this project, we study the properties of a non-trivial topological system which exhibits localized edge states. In our study, we adress the Kitaev chain, a one-dimensional chain of atoms deposited on top of a p-wave superconductor that…
The organization of the electrons in the ground state is classified by means of topological invariants, defined as global properties of the wavefunction. Here we address the Chern number of a two-dimensional insulator and we show that the…
Kitaev's sixteenfold way is a classification of exotic topological orders in which $\mathbb{Z}_2$ gauge theory is coupled to Majorana fermions of Chern number $C$. The $16$ distinct topological orders within this class, depending on $C \,…
We present a unified framework to construct and classify topological crystalline superconductors (TCSCs). The building blocks are one-dimensional topological superconductors (TSCs) protected solely by onsite symmetries, which are arranged…
Topological superconductivity in quasi-one-dimensional systems is a novel phase of matter with possible implications for quantum computation. Despite years of effort, a definitive signature of this phase in experiments is still debated. A…
Two-dimensional second-order topological superconductors (SOTSCs) have gapped bulk and edge states, with zero-energy Majorana bound states localized at corners. Motivated by recent advances in Majorana nanowire experiments, we propose to…
We investigate the robustness of topological phases in a Kitaev ladder composed of two coupled superconducting chains under the perturbing influence of a finite charge current. By introducing an effective Hamiltonian depending on the…
In this paper we introduce four Z_2 topological indices zeta_k=0,1 at k=(0,0), (0,pi), (pi, 0), (pi, pi) characterizing 16 universal classes of 2D superconducting states that have translation symmetry but may break any other symmetries. The…
We introduce a general scheme for constructing order parameters (OPs) by extracting generic patterns from the dominant Fock states of many-body ground states. While topological phases are traditionally characterized by non-local invariants,…
We study the phase transition of a star-shaped superconductor, which covers smoothly the range from zero to two dimensions with respect to the superconducting coherence length. Detailed measurements and numerical calculations show that the…
We have introduced a novel Majorana representation of S=1/2 spins using the Jordan-Wigner transformation and have shown that a generalized spin model of Kitaev defined on a brick-wall lattice is equivalent to a model of non-interacting…
Topological properties of quantum systems could provide protection of information against environmental noise, and thereby drastically advance their potential in quantum information processing. Most proposals for topologically protected…
Ordered phases of matter, such as solids, ferromagnets, superfluids, or quantum topological order, typically only exist at low temperatures. Despite this conventional wisdom, we present explicit local models in which all such phases persist…
This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…
The Kitaev honeycomb model is a paradigm of exactly-solvable models, showing non-trivial physical properties such as topological quantum order, abelian and non-abelian anyons, and chirality. Its solution is one of the most beautiful…
The modern understanding of topological insulators is based on Wannier obstructions in position space. Motivated by this insight, we study topological superconductors from a position-space perspective. For a one-dimensional superconductor,…
In this paper, the degenerate ground states of Z2 topological order on a plane with holes (the so-called surface codes) are used as the protected code subspace to build a topological quantum computer by tuning their quantum tunneling…
Topological superconductors are a class of unconventional superconducting materials featuring sub-gap zero-energy Majorana bound modes that hold promise as a building block for topological quantum computing. In this work, we study the…
Since the long range entanglement is a universal characteristic of topological quantum states belonging to the same class, a suitable mathematical representation of the long range entanglement has to be also universal. In this Letter, we…
In this general article, we map the one-dimensional transverse field quantum Ising model of ferromagnetism to Kitaev's one-dimensional p-wave superconductor, which has its application in fault-tolerant topological quantum computing. Mapping…