相关论文: Drinfeld Center as Quantum State Monodromy over Bl…

Topological protection is an elegant way of warranting the integrity of quantum and nanosized systems. In magnetism one example is the Bloch-point, a peculiar object implying the local vanishing of magnetization within a ferromagnet. Its…

Crystalline symmetry can be used to predict bulk and surface properties of topological phases. For non-interacting cases, symmetry-eigenvalue analysis of Bloch states at high symmetry points in the Brillouin zone simplifies the calculation…

We study the topological classification and related edge states of magnons in ferromagnets on honeycomb that can be described by a class of single-particle bosonic Bogoliubov-de Gennes (BdG) models. Both single layer and bilayer situations…

Bulk-boundary correspondence (BBC) of symmetry-protected topological (SPT) phases relates the non-trivial topological invariant of the bulk to the number of topologically protected boundary states. Recently, a finer classification of SPT…

Given a topological modular functor $\mathcal{V}$ in the sense of Walker \cite{Walker}, we construct vector bundles over $\bar{\mathcal{M}}_{g,n}$, whose Chern classes define semi-simple cohomological field theories. This construction…

In this dissertation, we detail an operator algebraic approach to studying topological order in the infinite volume setting. We give a thorough and self-contained review of the DHR-style approach on quantum spin systems, which builds a…

For a quantum state, or classical harmonic normal mode, of a system of spatial periodicity "R", Bloch character is encoded in a wavevector "K". One can ask whether this state has partial Bloch character "k" corresponding to a finer scale of…

New defects (Z-vortices and Nambu monopoles) are found to become thermodynamically relevant for the broken phase near to the (weakly first order) electroweak phase transition, and below the crossover for higher Higgs mass. The symmetric…

Spin-polarized reconstruction of the v=1 quantum Hall edge is accompanied by a spatial modulation of the charge density along the edge. We find that this is also the case for finite quantum Hall droplets: current spin density functional…

In this paper, we formulate the real-space Chern number in a supercell framework. In this framework, the overlap matrix between two corners of the Brillouin zone (BZ) is derived from diagonalizing the real-space Hamiltonian with periodic…

Bloch oscillations refer to the periodic oscillation of a wavepacket in a lattice under a constant force. Typically, the oscillation has a fundamental period that corresponds to the wavepacket traversing the first Brillouin zone once. Here…

We extend product Chern-Simons theory to develop several mixed $U(1)\times U(1)$ models where one gauge field is governed by a Chern-Simons term and the other by a Maxwell or Born-Infeld term. We show that, by choosing suitable potentials,…

We use a Bogoliubov-de Gennes (BdG) formulation to describe a single vortex in a neutral fermionic gas. It is presumed that the attractive pairing interaction can be arbitrarily tuned to exhibit a crossover from BCS to Bose-Einstein…

We describe the group of braided tensor autoequivalences of the Drinfeld centre of a finite group $G$ isomorphic to the identity functor (just as a functor) as a semi-direct product $Aut^1_{br}(\Z(G))\ \simeq\ Out_{2-cl}(G)\ltimes B(G)\ $…

Fully gapped two-dimensional superconductors coupled to dynamical electromagnetism are known to exhibit topological order. In this work, we develop a unified low-energy description for spin-singlet paired states by deriving topological…

Gapless quasiparticles can exist in the Bogoliubov-de Gennes (BdG) Hamiltonians in the mean field description of superconductors (SCs), fermionic superfluids (SFs) and quantum spin liquids (QSLs). The mechanism of gapless quasiparticles in…

The $\bf{g}$ tensor, which determines the reaction of Kramers-degenerate states to an applied magnetic field, is of increasing importance in the current design of spin qubits. It is affected by details of heterostructure composition,…

Based on geometric phases of Bloch electrons computed from first-principles, we propose a scheme for unambiguous partitioning of charge in matter, derivable directly from the Kohn-Sham states. Generalizing the fact that geometric phases…

We classify all connected and Lagrangian \'etale algebras in the Drinfeld center $\mathscr{Z}_1(\mathbf{2Vect}^\pi_G)$, where $G$ is a finite group and $\pi$ is a 4-cocycle on $G$. By D\'ecoppet's result every bosonic fusion 2-category…

Topological defects (such as monopoles, vortex lines, or domain walls) mark locations where disparate choices of a broken symmetry vacuum elsewhere in the system lead to irreconcilable differences. They are energetically costly (the energy…