Related papers: Homotopy Theoretic Classification of Symmetry Prot…
We propose that Symmetry Protected Topological Phases with a finite symmetry group G are classified by cobordism groups of the classifying space of G. This provides an explanation for the recent discovery of bosonic SPT phases which do not…
We use low-depth quantum circuits, a specific type of tensor networks, to classify two-dimensional symmetry-protected topological many-body localized phases. For (anti-)unitary on-site symmetries we show that the (generalized) third…
We study symmetry-protected topological (SPT) phases of matter in 2D protected by symmetries acting on fractal subsystems of a certain type. Despite the total symmetry group of such systems being subextensively large, we show that only a…
A number of proposals with differing predictions (e.g. Borel group cohomology, oriented cobordism, group supercohomology, spin cobordism, etc.) have been made for the classification of symmetry protected topological (SPT) phases. Here we…
We develop a theoretical framework for the classification and construction of symmetry protected topological (SPT) phases, which are a special class of zero-temperature phases of strongly interacting gapped quantum many-body systems that…
It has been proposed recently that interacting Symmetry Protected Topological (SPT) phases can be classified using cobordism theory. We test this proposal in the case of fermionic SPT phases with Z/2 symmetry, where Z/2 is either…
Vietoris-Rips and degree Rips complexes are represented as homotopy types by their underlying posets of simplices, and basic homotopy stability theorems are recast in these terms. These homotopy types are viewed as systems (or functors),…
This paper defines homology in homotopy type theory, in the process stable homotopy groups are also defined. Previous research in synthetic homotopy theory is relied on, in particular the definition of cohomology. This work lays the…
We consider the classification problem of symmetry protected topological (SPT) phases on quantum spin systems. SPT phases are gapped short-range-entangled quantum phases with a symmetry $G$. We explain that in one and two-dimensional…
We consider symmetry-protected topological (SPT) phases in 2D protected by linear subsystem symmetries, i.e. those that act along rigid lines. There is a distinction between a "strong" subsystem SPT phase, and a "weak" one, which is…
Motivated by the recent discovery of higher-order topological insulators, we study their counterparts in strongly interacting bosons: `higher-order symmetry protected topological (HOSPT) phases'. While the usual (1st-order) SPT phases in d…
We discuss the classification of SPT phases in condensed matter systems. We review Kitaev's argument that SPT phases are classified by a generalized cohomology theory, valued in the spectrum of gapped physical systems. We propose a concrete…
Symmetry Protected Topological (SPT) phases describe trivially-acting symmetries. We argue that a symmetry-based description of SPT phases ought to include the topological twist fields associated to the symmetry. Doing so allows us to…
Symmetry protected topological (SPT) states are bulk gapped states with gapless edge excitations protected by certain symmetries. The SPT phases in free fermion systems, like topological insulators, can be classified by the K-theory.…
This paper contains an overview of background from stable homotopy theory used by Freed--Hopkins in their work on invertible extended topological field theories. We provide a working guide to the stable homotopy category, to the Steenrod…
We make a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the frieze space groups in one dimension using matrix product states. Here, the spatial symmetries of the one-dimensional…
Recently, it has been shown that two-dimensional bosonic symmetry-protected topological(SPT) phases with on-site unitary symmetry $G$ can be completely classified by the group cohomology class $H^3(G, \mathrm{U}(1))$. Later, group…
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped phases in 1D systems can be completely characterized using tools related to projective representations of the…
Symmetry-protected topological (SPT) phases are short-range entangled phases of matter with a non-local order parameter which are preserved under a local symmetry group. Here, by using unsupervised learning algorithm, namely the diffusion…