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This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…

Numerical Analysis · Mathematics 2016-12-22 John P. Hollkamp , Mihir Sen , Fabio Semperlotti

In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that…

Strongly Correlated Electrons · Physics 2020-06-01 Yizhi You , Trithep Devakul , F. J. Burnell , S. L. Sondhi

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…

Strongly Correlated Electrons · Physics 2018-01-23 Gábor B. Halász , Timothy H. Hsieh , Leon Balents

We introduce lattice gauge theories which describe three-dimensional, gapped quantum phases exhibiting the phenomenology of both conventional three-dimensional topological orders and fracton orders, starting from a finite group $G$, a…

Strongly Correlated Electrons · Physics 2021-09-14 Nathanan Tantivasadakarn , Wenjie Ji , Sagar Vijay

Fracton topological order (FTO) is a new classification of correlated phases in three spatial dimensions with topological ground state degeneracy (GSD) scaling up with system size, and fractional excitations which are immobile or have…

Strongly Correlated Electrons · Physics 2021-12-10 Ting Fung Jeffrey Poon , Xiong-Jun Liu

We introduce a stabilizer code model with a qutrit at every edge on a square lattice and with non-invertible plaquette operators. The degeneracy of the ground state is topological as in the toric code, and it also has the usual deconfined…

High Energy Physics - Theory · Physics 2024-11-28 Tanay Kibe , Ayan Mukhopadhyay , Pramod Padmanabhan

We study the decoding transition for quantum error correcting codes with the help of a mapping to random-bond Wegner spin models. Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both known…

Quantum Physics · Physics 2014-02-11 Alexey A. Kovalev , Leonid P. Pryadko

We study classical and quantum LDPC codes of constant rate obtained by the lifted product construction over non-abelian groups. We show that the obtained families of quantum LDPC codes are asymptotically good, which proves the qLDPC…

Information Theory · Computer Science 2022-01-24 Pavel Panteleev , Gleb Kalachev

We broaden the scope of quantum field theory by introducing a general class of discrete gauge theories that realize either topological order or fracton behavior across dimensions. We start from translation-invariant systems endowed with…

Strongly Correlated Electrons · Physics 2026-01-21 Guilherme Delfino , Claudio Chamon , Yizhi You

The study of gapped quantum many-body systems in three spatial dimensions has uncovered the existence of quantum states hosting quasiparticles that are confined, not by energetics but by the structure of local operators, to move along lower…

Strongly Correlated Electrons · Physics 2019-11-06 Daniel Bulmash , Maissam Barkeshli

Fracton topological phases host fractionalized topological quasiparticles with restricted mobility, with promising applications to fault-tolerant quantum computation. While a variety of exactly solvable fracton models have been proposed,…

Strongly Correlated Electrons · Physics 2019-08-21 Yizhi You , Felix von Oppen

Fracton topological order describes a remarkable phase of matter which can be characterized by fracton excitations with constrained dynamics and a ground state degeneracy that increases exponentially with the length of the system on a…

Strongly Correlated Electrons · Physics 2017-10-06 Kevin Slagle , Yong Baek Kim

Discrete time crystals (DTCs) are nonequilibrium phases of matter characterized by robust subharmonic order parameter dynamics. We report a new type of DTC in a periodically driven surface code, the subharmonic signature of which is only…

Quantum Physics · Physics 2021-08-04 Raditya Weda Bomantara

Low-depth parity check (LDPC) codes are a paradigm of error correction that allow for spatially non-local interactions between (qu)bits, while still enforcing that each (qu)bit interacts only with finitely many others. On expander graphs,…

Quantum Physics · Physics 2023-10-25 Tibor Rakovszky , Vedika Khemani

We investigate the iterative construction of discrete Laplacians on 2D square lattices, revealing emergent fractal-like patterns shaped by modular arithmetic. While classical 2222-style iterations reproduce known structures such as the…

Dynamical Systems · Mathematics 2026-03-16 Małgorzata Nowak-Kępczyk

Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable…

Strongly Correlated Electrons · Physics 2023-05-30 Guo-Yi Zhu , Ji-Yao Chen , Peng Ye , Simon Trebst

This study proposes a method for producing an infinite number of fractals using aperiodic substitution tilings, exemplified by the Ammann Chair tiling. Higher-order substitutions of aperiodic tilings are utilized in relation to the…

Metric Geometry · Mathematics 2023-05-19 Kah Heng Lee

Fractal patterns are observed in computational mechanics of elastic-plastic transitions in two models of linear elastic/perfectly-plastic random heterogeneous materials: (1) a composite made of locally isotropic grains with weak random…

Statistical Mechanics · Physics 2015-05-13 J. Li , M. Ostoja-Starzewski

We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, point-like topological excitations, and sub-extensive topological degeneracy. We demonstrate a…

Strongly Correlated Electrons · Physics 2017-01-04 Sagar Vijay , Jeongwan Haah , Liang Fu

Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or…

Analysis of PDEs · Mathematics 2021-10-08 Marta D'Elia , Mamikon Gulian , Hayley Olson , George Em Karniadakis