相关论文: Emergent fermionic gauge theory and foliated fract…

We consider fermionic systems in which fermion parity is conserved within rigid subsystems, and describe an explicit procedure for gauging such subsystem fermion parity symmetries to obtain bosonic spin Hamiltonians. We show that gauging…

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…

Fracton order is an intriguing new type of order which shares many common features with topological order, such as topology-dependent ground state degeneracies, and excitations with mutual statistics. However, it also has several…

Based on several previous examples, we summarize explicitly the general procedure to gauge models with subsystem symmetries, which are symmetries with generators that have support within a sub-manifold of the system. The gauging process can…

In the study of three-dimensional gapped models, two-dimensional gapped states should be considered as a free resource. This is the basic idea underlying the notion of `foliated fracton order' proposed in Phys. Rev. X 8, 031051 (2018). We…

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…

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…

Inspired by recent developments generalizing Jordan-Wigner dualities to higher dimensions, we develop a framework of such dualities using an algebraic formalism for translation-invariant Hamiltonians proposed by Haah. We prove that given a…

2+1D multi-component $U(1)$ gauge theories with a Chern-Simons (CS) term provide a simple and complete characterization of 2+1D Abelian topological orders. In this paper, we extend the theory by taking the number of component gauge fields…

We analyze the "higher rank" gauge theories, that capture some of the phenomenology of the Fracton order. It is shown that these theories lose gauge invariance when arbitrarily weak and smooth curvature is introduced. We propose a…

We study the conformal window of gauge theories containing fermionic matter fields, where the gauge group is any of the exceptional groups with the fermions transforming according to the fundamental and adjoint representations and the…

Topologically-ordered phases of matter, although stable against local perturbations, are usually restricted to relatively small regions in phase diagrams. Their preparation requires thus a precise fine tunning of the system's parameters, a…

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.…

Lattice gauge theories are a powerful language to theoretically describe a variety of strongly correlated systems, including frustrated magnets, high-$T_c$ superconductors, and topological phases. However, in many cases gauge fields couple…

We consider quantum error-correcting subsystem codes whose gauge generators realize a translation-invariant, free-fermion-solvable spin model. In this setting, errors are suppressed by a Hamiltonian whose terms are the gauge generators of…

Fractons are gapped point-like excitations in $d=3$ topological ordered phases whose motion is constrained. They have been discovered in several gapped models but a unifying physical mechanism for generating them is still missing. It has…

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…

We give another reformulation of the Thirring model (with four-fermion interaction of the current-current type) as a gauge theory and identify it with a gauge-fixed version of the corresponding gauge theory according to the Batalin-Fradkin…

We propose a renormalizable model with no fundamental scalars which breaks itself in the manner of a "tumbling" gauge theory down to the standard model with a top-quark condensate. Because of anomaly cancellation requirements, this model…

The objective of the present work -- a literature review on both gapped and gapless fractonic theories -- is to pedagogically fill in the gaps between the research on fractons, and an undergraduate physics education (particularly quantum…