Related papers: Augmentation and Bulk Edge Correspondence for one …
A method for finding the exact analytical solutions for the bulk and edge energy levels and corresponding eigenstates for all commensurate Aubry-Andr\'e/Harper single-particle models under open boundary conditions is presented here, both…
Maxwell lattices are characterized by an equal number of degrees of freedom and constraints. A subset of them, dubbed topological lattices, are capable of localizing stress and deformation on opposing edges, displaying a polarized…
Dense networks with weighted connections often exhibit a community like structure, where although most nodes are connected to each other, different patterns of edge weights may emerge depending on each node's community membership. We…
Using bulk gapless topological superconductors in both 1d and 2d as free fermion model examples, we demonstrate the power of subsystem correlation spectrum (the spectrum of correlation matrix), or equivalently the entanglement spectrum for…
Despite the extensive studies of topological states, their characterization in strongly nonlinear classical systems has been lacking. In this work, we identify the proper definition of Berry phase for nonlinear bulk modes and characterize…
A well-defined local non-Abelian gauge connection involving a rank-p gauge B-field was introduced a decade ago. This was achieved by introducing doublet groups and doublet-assembled connections that can act on a doublet of matter fields,…
We introduce the Density Formula for (topological) drawings of graphs in the plane or on the sphere, which relates the number of edges, vertices, crossings, and sizes of cells in the drawing. We demonstrate its capability by providing…
By developing a generalized cobordism theory, we explore the higher global symmetries and higher anomalies of quantum field theories and interacting fermionic/bosonic systems in condensed matter. Our essential math input is a generalization…
Graph augmentation methods play a crucial role in improving the performance and enhancing generalisation capabilities in Graph Neural Networks (GNNs). Existing graph augmentation methods mainly perturb the graph structures, and are usually…
We provide an upper bound on the Cheeger constant and first eigenvalue of the Laplacian of a finite-volume hyperbolic 3-manifold M, in terms of data from any surgery diagram for M. This has several consequences. We prove that a family of…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
We study in detail the relationship between strong subadditivity for a boundary field theory and energy conditions for its bulk dual in 2+1 dimensions. We provide a discussion of known facts and new results organized from the simplest case…
We prove a general theorem on the relation between the bulk topological quantum number and the edge states in two dimensional insulators. It is shown that whenever there is a topological order in bulk, characterized by a non-vanishing Chern…
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…
The bulk-edge correspondence is one of the most important ingredients in the theory of topological phases of matter. While the bulk-edge correspondence is applicable for Hermitian junction systems where two subsystems with independent…
We develop a general incremental framework for hyperelastic solids whose surfaces exhibit both stretch-dependent and curvature-dependent elastic behavior. Building upon a variational formulation of curvature-dependent surface elasticity, we…
We formulate the tight-binding model for cubic $\alpha$-Sn based on the DFT calculations. In the model, we incorporate a variable bond angle, which allows us to simulate the effect of the in-plane strain. In the bulk, we demonstrate the…
In quenching a topological phase across phase transition, the dynamical bulk-surface correspondence emerges that the bulk topology of $d$-dimensional ($d$D) phase relates to the nontrivial pattern of quench dynamics emerging on $(d-1)$D…
We investigate the reflected entropy for bipartite mixed state configurations in a $T\bar{T}$ deformed boundary conformal field theory in $2$ dimensions (BCFT$_2$). The bulk dual is described by asymptotically AdS$_3$ geometries with the…
Topology is quickly becoming a cornerstone in our understanding of electronic systems. Like their electronic counterparts, bosonic systems can exhibit a topological band structure, but in real materials it is difficult to ascertain their…