Related papers: Composing topological domain walls and anyon mobil…
We supply basic tools for the study of the topological order of a multiplet which is an eigenspace of a finite-dimensional normal operator with continuous parameters. We allow intrinsic degeneracies within the multiplet where a well-known…
This paper discusses the relationships between gauge theories defined by gauge groups with finite trivially-acting centers, and theories with restrictions on nonperturbative sectors, in two and four dimensions. In two dimensions, these…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
Topological insulators exhibit boundary states protected by bulk band topology, a principle first established in quantum systems and later extended to classical waves, including phononics. Conventionally, an $n$-dimensional bulk with…
A long-standing problem in the study of topological phases of matter has been to understand the types of fractional topological insulator (FTI) phases possible in 3+1 dimensions. Unlike ordinary topological insulators of free fermions, FTI…
Topology is being widely adopted to understand and to categorize quantum matter in modern physics. The nexus of topology orders, which engenders distinct quantum phases with benefits to both fundamental research and practical applications…
We examine the various linkings in space-time of ``ball-like'' and ``ring-like'' topological solitons in certain nonlinear sigma models in 2+1 and 3+1 dimensions. By going to theories where soliton overlaps are forbidden, these linkings…
We develop a theoretical framework for the classification and construction of symmetry protected topological (SPT) phases, which are a special class of zero-temperature phases of strongly interacting gapped quantum many-body systems that…
We consider a mean-field Hamiltonian for a $d_{x^2-y^2}+(p+ip)$ superconductor(SC) in presence of spin-density-wave(SDW) order. This is due to the fact that the non-commutativity of any two orders produces the third one. The energy spectrum…
Two new recently proposed classes of topological phases, namely fractons and higher order topological insulators (HOTIs), share at least superficial similarities. The wide variety of proposals for these phases calls for a universal field…
I report on some work in progress on the dynamics of extended objects in field theories after a rapid phase transition, as is relevant in the early Universe. An analytic technique, originally introduced to approximate the dynamics of…
A topological phase can undergo a phase transition driven by anyon condensation. A potential obstruction to such a mechanism could arise if there exists a symmetry between anyons that have non-trivial mutual statistics. Here we consider…
The detection of topological phases of matter becomes a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or…
We give a mathematical definition of a gapped domain wall between topological phases and a gapped boundary of a topological phase. We then provide answers to some recent questions studied by Lan, Wang and Wen in condensed matter physics…
The evolution of the physical properties of two-dimensional material from monolayer limit to the bulk reveals unique consequences from dimension confinement and provides a distinct tuning knob for applications. Monolayer 1T'-phase…
When can two strongly rational vertex operator algebras or 1+1d rational conformal field theories (RCFTs) be related by topological manipulations? For vertex operator algebras, the term "topological manipulations" refers to operations like…
The topology of an insulator can be defined even when all eigenstates of the system are localized - an extreme case of Anderson insulators that we call ultra-localized. We derive the classification of such ultra-localized insulators in all…
Topological phononic crystals, alike their electronic counterparts, are characterized by a bulk-edge correspondence where the interior of a material dictates the existence of stable surface or boundary modes. In the mechanical setup, such…
We study multiplicities and junctions of BPS domain walls interpolating between different chiral vacua in $\mathcal{N}=1$ supersymmetric QCD (SQCD) with the SU$(N)$ gauge group and a varying number of fundamental quarks. Depending on the…
Weyl semimetals and higher-order topological insulators represent two fundamental yet distinct classes of topological matter. While both have been extensively studied in classical-wave systems, their coexistence and controllable transition…