Related papers: One dimensional gapped quantum phases and enriched…
We define a symmetric monoidal (4,3)-category with duals whose objects are certain enriched multi-fusion categories. For every modular tensor category $\mathcal{C}$, there is a self enriched multi-fusion category $\mathfrak{C}$ giving rise…
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…
We present commuting projector Hamiltonian realizations of a large class of (3+1)D topological models based on mathematical objects called unitary G-crossed braided fusion categories. This construction comes with a wealth of examples from…
We characterize injective objects, injective hulls and essential embeddings in the category of symmetric categories enriched in a small, integral and involutive quantaloid. In particular, injective partial metric spaces are precisely…
We study fermionic non-invertible symmetries in (1+1)d, which are generalized global symmetries that mix fermion parity symmetry with other invertible and non-invertible internal symmetries. Such symmetries are described by fermionic fusion…
We witness multipartite entanglement in the Kitaev chain -- a benchmark model of one dimensional topological insulator -- also with variable-range pairing, using the quantum Fisher information. Phases having a finite winding number, both…
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…
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…
We establish a comprehensive framework for characterizing the infrared (IR) phases of a fermionic quantum theory in three spatial dimensions, based on its quantum anomalies associated with a finite symmetry. We uncover a fundamental…
This is the first of a series of papers on enriched infinity categories, seeking to reduce enriched higher category theory to the higher algebra of presentable infinity categories, which is better understood and can be approached via…
Quantum many-body systems divide into a variety of phases with very different physical properties. The question of what kind of phases exist and how to identify them seems hard especially for strongly interacting systems. Here we make an…
We investigate the diagonal entropy for ground states of the extended Kitaev chains with extensive pairing and hopping terms. The systems contain rich topological phases equivalently represented by topological invariant winding numbers and…
We sketch a procedure to capture general non-invertible symmetries of a d-dimensional quantum field theory in the data of a higher-category, which captures the local properties of topological defects associated to the symmetries. We also…
We give a classification of gapped quantum phases of one-dimensional systems in the framework of Matrix Product States (MPS) and their associated parent Hamiltonians, for systems with unique as well as degenerate ground states, and both in…
We discuss several useful interpretations of the categorical dimension of objects in a braided fusion category, as well as some conjectures demonstrating the value of quantum dimension as a quantum statistic for detecting certain behaviors…
We examine the interplay of symmetry and topological order in $2+1$ dimensional fermionic topological phases of matter. We define fermionic topological symmetries acting on the emergent topological effective theory described using braided…
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…
We initiate the S-matrix bootstrap analysis of theories with non-invertible symmetries in (1+1) dimensions. Our previous work showed that crossing symmetry of S-matrices in such theories is modified, with modification characterized by the…
We construct a state-sum type invariant of smooth closed oriented $4$-manifolds out of a $G$-crossed braided spherical fusion category ($G$-BSFC) for $G$ a finite group. The construction can be extended to obtain a $(3+1)$-dimensional…
In fairly elementary terms this paper presents, and expands upon, a recent result by Garner by which the notion of topologicity of a concrete functor is subsumed under the concept of total cocompleteness of enriched category theory.…