Related papers: Composing topological domain walls and anyon mobil…

Much of the dramatic growth in research on topological materials has focused on topologically protected surface states. While the domain walls of topological materials such as Weyl semimetals with broken inversion or time-reversal symmetry…

The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…

Domain wall junctions are studied in N=2 supersymmetric U(Nc) gauge theory with Nf(>Nc) flavors. We find that all three possibilities are realized for positive, negative and zero junction charges. The positive junction charge is found to be…

We explore novel topological responses and axion-like phenomena in three-dimensional insulating systems with spacetime-dependent mass terms encoding domain walls. Via a dimensional-reduction approach, we derive a new axion-electromagnetic…

Modulated symmetries are internal symmetries which do not commute with spatial symmetries; dipolar symmetries are a prime example. We give a general recipe for constructing topological phases protected by modulated symmetries via a defect…

We review the dimensional reduction procedure in the group cohomology classification of bosonic SPT phases with finite abelian unitary symmetry group. We then extend this to include general reductions of arbitrary dimensions and also extend…

We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we…

We provide a new perspective on fracton topological phases, a class of three-dimensional topologically ordered phases with unconventional fractionalized excitations that are either completely immobile or only mobile along particular lines…

In these decades, it has been gradually established that edge modes of a wide class of topologically ordered systems are governed by the bulk-edge correspondence and anyon condensation. The former has been studied many times because it can…

It is well-known that many topological phase transitions of intrinsic Abelian topological phases are accompanied by condensation and confinement of anyons. However, for non-Abelian topological phases, more intricate phenomena can occur at…

We investigate the interplay of generalized global symmetries in 2+1 dimensions in a lattice model that couples a $\mathbb{Z}_N$ clock model to a $\mathbb{Z}_N$ gauge theory via a topological interaction. This coupling binds the charges of…

We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive…

The moduli space of gapped Hamiltonians that are in the same topological phase is an intrinsic object that is associated to the topological order. The topology of these moduli spaces is used recently in the construction of Floquet codes. We…

We derive a series of quantitative bulk-boundary correspondences for 3D bosonic and fermionic symmetry-protected topological (SPT) phases under the assumption that the surface is gapped, symmetric and topologically ordered, i.e., a…

Getting precise aspects of road through segmentation from remote sensing imagery is useful for many real-world applications such as autonomous vehicles, urban development and planning, and achieving sustainable development goals. Roads are…

In this work, we introduce a new type of topological order which is protected by subsystem symmetries which act on lower dimensional subsets of lattice many-body system, e.g. along lines or planes in a three dimensional system. The symmetry…

Topological phases of matter are commonly understood as emerging either from crystalline symmetry and intrinsic spin-orbit coupling or from disorder-driven electronic renormalization. In realistic materials, however, structural defects…

Topological phases exhibit unconventional order that cannot be detected by any local order parameter. In the framework of Projected Entangled Pair States(PEPS), topological order is characterized by an entanglement symmetry of the local…

We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of representation theory in terms of tensor categories is…

Topological orders are new phases of matter beyond Landau symmetry breaking. They correspond to patterns of long-range entanglement. In recent years, it was shown that in 1+1D bosonic systems there is no nontrivial topological order, while…