Related papers: Universal Wave Function Overlap and Universal Topo…
A universal topological marker has been proposed recently to map the topological invariants of Dirac models in any dimension and symmetry class to lattice sites. Using this topological marker, we examine the conditions under which the…
We define topological invariants in terms of the ground states wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magneto-electric $\theta$ term in…
Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…
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…
In this article we consider large data Wave-Maps from $\mathbb{R}^{2+1}$ into a compact Riemannian manifold $(\mathcal{M},g)$, and we prove that regularity and dispersive bounds persist as long as a certain type of bulk (non-dispersive)…
We develop a generalized covering space theory for a class of uniform spaces called coverable spaces. Coverable spaces include all geodesic metric spaces, connected and locally pathwise connected compact topological spaces, in particular…
Symmetry topological field theory (SymTFT) gives a holographic correspondence between systems with a global symmetry and a higher-dimensional topological field theory. In this framework, classification of gapped phases of matter in…
We prove local and global existence from large, rough initial data for a wave map between 1+1 dimensional Minkowski space and an analytic manifold. Included here is global existence for large data in the scale-invariant norm $\dot L^{1,1}$,…
A generalized symmetry (defined by the algebra of local symmetric operators) can go beyond group or higher group description. A theory of generalized symmetry (up to holo-equivalence) was developed in terms of symmetry-TO -- a bosonic…
We establish universality of the renormalised energy for mappings from a planar domain to a compact manifold, by approximating subquadratic polar convex functionals of the form $\int_\Omega f(|\mathrm{D} u|)\,\mathrm{d} x$. The analysis…
The study of spatial symmetries was accomplished during the last century, and had greatly improved our understanding of the properties of solids. Nowadays, the symmetry data of any crystal can be readily extracted from standard…
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped phases in 1D systems can be completely characterized using tools related to projective representations of the…
We investigate topological properties of density matrices motivated by the question to what extent phenomena like topological insulators and superconductors can be generalized to mixed states in the framework of open quantum systems. The…
We study topological properties of density wave states with broken translational symmetry in two-dimensional multi-orbital systems with a particular focus on t$_{2g}$ orbitals in square lattice. Due to distinct symmetry properties of…
Quantum entanglement is a particularly useful characterization of topological orders which lack conventional order parameters. In this work, we study the entanglement in topologically ordered states between two arbitrary spatial regions,…
We formalize and generalize the concept of a topological state-sum construction using the language of tensor networks. We give examples for constructions that are possibly more general than all state-sum constructions in the literature that…
\citet{Shmuel2016JMPS} discovered that all infinite band structures of waves at normal incidence in two-phase laminates are encapsulated in a compact universal manifold. We show that manifolds of higher dimensionality encapsulate the band…
We introduce exactly solvable gapless quantum systems in $d$ dimensions that support symmetry protected topological (SPT) edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as…
The Mapper algorithm, a technique within topological data analysis (TDA), constructs a simplified graphical representation of high-dimensional data to uncover its underlying shape and structural patterns. The algorithm has attracted…
We establish a holographic duality between d-dimensional mixed-state symmetry-protected topological phases (mSPTs) and (d+1)-dimensional subsystem symmetry-protected topological states (SSPTs). Specifically, we show that the reduced density…