Related papers: Fracton models from product codes
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…
We introduce a class of gapped three-dimensional models, dubbed "cage-net fracton models," which host immobile fracton excitations in addition to non-Abelian particles with restricted mobility. Starting from layers of two-dimensional…
Motivated by the inadequacy of conducting atomistic simulations of crack propagation using static boundary conditions that do not reflect the movement of the crack tip, we extend Sinclair's flexible boundary condition algorithm [Philos.…
There is a growing interest in searching for topology in fractal dimensions with the aim of finding different properties and advantages compared to the integer dimensional case. It has previously been shown that the Laughlin state can be…
We consider the local rank-modulation scheme in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. The local rank-modulation, as a generalization of the rank-modulation scheme, has been…
A mechanical model is introduced for predicting the initiation and evolution of complex fracture patterns without the need for a damage variable or law. The model, a continuum variant of Newton's second law, uses integral rather than…
We demonstrate how pump-probe techniques enable specific diagnostics of fracton phases of matter by exploring how lineon-planon braiding in the paradigmatic X-cube phase may be probed spectroscopically. Our discussion builds on works…
The manipulation of topologically-ordered phases of matter to encode and process quantum information forms the cornerstone of many approaches to fault-tolerant quantum computing. Here we demonstrate that fault-tolerant logical operations in…
We consider the numerical homogenization of a class of fractal elliptic interface problems inspired by related mechanical contact problems from the geosciences. A particular feature is that the solution space depends on the actual fractal…
A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. The ordering comes in the classical case from a coupling of 2D layers and in the quantum model…
A promising route towards the realization of chiral spin liquids is the quantum melting of classically noncoplanar spin states via quantum fluctuations. In the classical realm, such noncoplanar orders can effectively be stabilized by…
We construct linear codes over the finite field Fq from arbitrary simplicial complexes, establishing a connection between topological properties and fundamental coding parameters. First, we study the behaviour of the weights of codewords…
In this article, new regular incidence structures are presented. They arise from sets of conics in the affine plane blown-up at its rational points. The LDPC codes given by these incidence matrices are studied. These sparse incidence…
We introduce a $\mathbb{Z}_N$ stabilizer code that can be defined on any spatial lattice of the form $\Gamma\times C_{L_z}$, where $\Gamma$ is a general graph. We also present the low-energy limit of this stabilizer code as a Euclidean…
We present a theoretical and computational framework based on fractional calculus for the analysis of the nonlocal static response of cylindrical shell panels. The differ-integral nature of fractional derivatives allows an efficient and…
The hard exclusive electroproduction processes provide new information about hadronic structure accumulated in nonforward parton distributions. The NFPD's are universal hybrid functions having the properties of parton densities, hadronic…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
We find that the overlapping of a topological quantum color code state, representing a quantum memory, with a factorized state of qubits can be written as the partition function of a 3-body classical Ising model on triangular or Union Jack…
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…
Experimental evidence for the generation of intrinsic localized modes (ILMs) in a nonlinear electrical transmission line is presented both via modulational instability (MI) of the uniform mode and via driving the lattice locally. The…