Related papers: Planon-modular fracton orders
The decomposition matrix of a finite group in prime characteristic p records the multiplicities of its p-modular irreducible representations as composition factors of the reductions modulo p of its irreducible representations in…
We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by particle-like excitations exhibiting exotic braiding…
This study presents the formulation, the numerical solution, and the validation of a theoretical framework based on the concept of variable-order mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle solids. More…
In these lectures we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. A subfactor with a braiding determines a matrix $Z$ which is obtained as a coupling…
The causal graph of a planning instance is an important tool for planning both in practice and in theory. The theoretical studies of causal graphs have largely analysed the computational complexity of planning for instances where the causal…
We review a burgeoning field of "fractons" -- a class of models where quasi-particles are strictly immobile or display restricted mobility that can be understood through generalized multipolar symmetries and associated conservation laws.…
We study a broad class of qudit stabilizer codes, termed $\mathbb{Z}_N$ bivariate-bicycle (BB) codes, arising either as two-dimensional realizations of modulated gauge theories or as $\mathbb{Z}_N$ generalizations of binary BB codes. Our…
Fracton phases exhibit striking behavior which appears to render them beyond the standard topological quantum field theory (TQFT) paradigm for classifying gapped quantum matter. Here, we explore fracton phases from the perspective of defect…
A self-organization is an universal phenomenon in nature and, in particular, is highly important in materials systems and biology. We proposed a new theory that allowed us to model the most challenging cases of atomic self-assembling whose…
We study constrained percolation models on planar lattices including the $[m,4,n,4]$ lattice and the square tilings of the hyperbolic plane, satisfying certain local constraints on faces of degree 4, and investigate the existence of…
Fracton phases of matter are gapped phases of matter that, by dint of their sensitivity to UV data, demand non-standard quantum field theories to describe them in the IR. Two such approaches are foliated quantum theory and exotic field…
We propose a set of constraints on the ground-state wavefunctions of fracton phases, which provide a possible generalization of the string-net equations used to characterize topological orders in two spatial dimensions. Our constraint…
The bulk-boundary correspondence is a hallmark feature of topological phases of matter. Nonetheless, our understanding of the correspondence remains incomplete for phases with intrinsic topological order, and is nearly entirely lacking for…
This is the first paper of a series of three, reporting on numerical simulation studies of geometric and mechanical properties of static assemblies of spherical beads under an isotropic pressure. Frictionless systems assemble in the unique…
We use a local model to study the formation and the structure of the low energy charge transfer excitations in the insulating Cu-O$_2$ plane. The elementary excitation is a bound exciton of spin singlet, consisting of a Cu$^+$ and a…
Motivated by recent neutron scattering experiments on the cuprate superconductors, we present a phenomenological framework describing the dynamics of collective spin excitations coupled to charge/bond order fluctuations. Our quantum lattice…
We introduce the logic FOCN(P) which extends first-order logic by counting and by numerical predicates from a set P, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature. We…
Contrary to a broadly accepted assumption we show that random (Ga,In)P is not an exception with respect to the crude classification of the phonon mode behavior of random mixed crystals in terms of 1-bond->1-mode systems or 2-bond->1-mode…
The emerging study of fractons, a new type of quasi-particle with restricted mobility, has motivated the construction of several classes of interesting continuum quantum field theories with novel properties. One such class consists of…
Classical configurations in the CP^{N-1} model on R^1 x S^1 is studied with twisted boundary conditions. Starting from fractional instantons with the Z_N twisted boundary conditions, we review briefly the relevance of our study to…