Related papers: Symmetric approximant formalism for statistical to…
Symmetry-protected topological (SPT) phases are short-range entangled quantum states characterized by anomalous edge behavior, a manifestation of the bulk-boundary correspondence for topological phases. Moreover, the Li-Haldane conjecture…
Although the richness of spatial symmetries has led to a rapidly expanding inventory of possible topological crystalline (TC) phases of electrons, physical realizations have been slow to materialize due to the practical difficulty to…
Topological insulators as new type of quantum matter materials are characterized by a full insulating gap in the bulk and gapless edge/surface states which are protected by time-reversal symmetry. We propose the interference patterns caused…
Thermodynamically consistent measurements can either preserve statistics (unbiased) or preserve marginal states (non-invasive) but not both. Here we show the existence of metrological tasks which unequally favor each of the aforementioned…
The spectral localizer is a predictive framework for the computation of topological invariants of natural and artificial materials. Here, three crucial improvements on the criterion for the validity of the framework are reported: first,…
Symmetry protected topological (SPT) phases of bosons in $d$ spatial dimensions have been characterized by the action of the protecting global symmetry $G$ on their boundary. The symmetry acts on the boundary in a way that would be…
A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…
Crystalline topological insulators owe their topological character to the protection that certain boundary states acquire because of certain point-group symmetries. We first show that a Hermitian operator obeying supersymmetric quantum…
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
We review the dimensional reduction procedure in the group cohomology classification of bosonic SPT phases with finite abelian unitary symmetry group. We then extend this to include general reductions of arbitrary dimensions and also extend…
The S-matrix invariant is known to be complete for translation invariant topological stabilizer models in two spatial dimensions, as such models are phase equivalent to some number of copies of toric code. In three dimensions, much less is…
Topological entropy is a widely studied indicator of chaos in topological dynamics. Here we give a generalized definition of topological entropy which may be applied to set-valued functions. We demonstrate that some of the well-known…
Topological invariants are conventionally known to be responsible for protection of extended states against disorder. A prominent example is the presence of topologically protected extended-states in two-dimensional (2D) quantum Hall…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
Topological data analysis provides a collection of tools to encapsulate and summarize the shape of data. Currently it is mainly restricted to \emph{mapper algorithm} and \emph{persistent homology}. In this paper we introduce new…
In this article, we study quantum critical phenomena in surfaces of symmetry-protected topological matter, i.e. surface topological quantum criticality. A generic phase boundary of gapless surfaces in a symmetry-protected state shall be a…
Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly…
Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the…
Higher-order topological insulators have attracted significant interest in recent years. However, identifying a universal topological invariant capable of characterizing higher-order topology remains challenging. Here, we propose a…
The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model…