Related papers: Classification of equivariant quasi-local automorp…

We consider general fermionic quantum field theories with a global finite group symmetry $G$, focusing on the case of 2-dimensions and torus spacetime. The modular transformation properties of the family of partition functions with…

In this paper, we study the diagrammatic categorification of the fermion algebra. We construct a graphical category corresponding to the one-dimensional fermion algebra, and we investigate the properties of this category. The categorical…

We present a systematic topological classification of fermionic and bosonic topological phases protected by time-reversal, particle-hole, parity, and combination of these symmetries. We use two complementary approaches: one in terms of…

We calculated the spectral properties of two related families of non-Hermitian free-particle quantum chains with $N$-multispin interactions ($N=2,3,\ldots$). The first family have a $Z(N)$ symmetry and are described by free parafermions.…

We classify local unitary equivalence classes of symmetric states via a classification of their local unitary stabilizer subgroups. For states whose local unitary stabilizer groups have a positive number of continuous degrees of freedom,…

We prove that the cyclic chain complex of the categorical coalgebra of singular chains on an arbitrary topological space $X$ is naturally quasi-isomorphic to the $S^1$-equivariant chains of the free loop space of $X$. This statement does…

Let G be a finite group. We study the group of G-equivariant self-homotopy equivalences of product of G-spaces. For a product of n-spaces, we represent it as product of n-subgroups under the assumption of equivariant reducibility. Further…

In recent years, fermionic topological phases of quantum matter has attracted a lot of attention. In a pioneer work by Gu, Wang and Wen, the concept of equivalence classes of fermionic local unitary(FLU) transformations was proposed to…

The problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general…

Classifying phases of local quantum systems is a general problem that includes special cases such as free fermions, commuting projectors, and others. An important distinction in this classification should be made between classifying…

For a relatively minimal surface fibration $f: X\to C$, the equivariant automorphism group of $f$ is, roughly speaking, the group of automorphisms of $X$ preserving the fibration structure. We present a classification of such fibrations of…

Automorphic loops are loops in which all inner mappings are automorphisms. A large class of automorphic loops is obtained as follows: Let $m$ be a positive even integer, $G$ an abelian group, and $\alpha$ an automorphism of $G$ that…

We discuss the relationship between (co)homology groups and categorical diagonalization. We consider the category of chain complexes in the category of finitely generated free modules on a commutative ring. For a fixed chain complex with…

This work takes place over a conformally flat spin manifold (M,g). We prove existence and uniqueness of the conformally equivariant quantization valued in spinor differential operators, and provide an explicit formula for it when restricted…

We study the behaviour of continuous automorphism groups of quantum spin systems on the lattice. Whereas the shift is norm asymptotically abelian continuous automorphism groups can lead only to delocalization but not to norm asymptotic…

The partial automorphisms of a graph $X$ having $N$ vertices are the bijections $\sigma:I\to J$ with $I,J\subset\{1,\ldots,N\}$ which leave invariant the edges. These bijections form a semigroup $\widetilde{G}(X)$, which contains the…

We establish the existence of a topological classification of many-particle quantum systems undergoing unitary time evolution. The classification naturally inherits phenomenology familiar from equilibrium -- it is robust against disorder…

We examine the graded automorphism groups of quantum affine spaces and classify these groups for spaces of dimension 7 or less. Using permutation actions on partitions, we investigate cases when the group decomposes as a product of graded…

We study fermionic fields localized on topologically unstable domain walls bounded by strings in a grand unified theory theoretical framework. Particularly, we found that the localized fermionic degrees of freedom, which are up and down…

We determine the quantum automorphism groups of finite graphs. These are quantum subgroups of the quantum permutation groups defined by Wang. The quantum automorphism group is a stronger invariant for finite graphs than the usual one. We…