Related papers: Generalized topological state-sum constructions an…
Gapped phases in 2+1 dimensional quantum field theories with fusion 2-categorical symmetries were recently classified and characterized using the Symmetry Topological Field Theory (SymTFT) approach arXiv:2408.05266, arXiv:2502.20440. In…
We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…
The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…
A number of recent articles have reported the existence of topologically non-trivial states and associated end states in one-dimensional incommensurate lattice models that would usually only be expected in higher dimensions. Using an…
We study criteria for and properties of boundary-to-boundary holography in a class of spin network states defined by analogy to projected entangled pair states (PEPS). In particular, we consider superpositions of states corresponding to…
We introduce the theory of generalised ultracategories, these are relational extensions to ultracategories as defined by Lurie. An essential example of generalised ultracategories are topological spaces, and these play a fundamental role in…
We construct a ring structure on complex cobordism tensored with the rationals, which is related to the usual ring structure as quantum cohomology is related to ordinary cohomology. The resulting object defines a generalized two-…
The paper studies a general scheme for constructing metrics on a product of metric spaces by means of a family of continuous convex functions. This construction includes the conventional $p$-metrics and generates metrics that are…
This thesis is divided into two mainly independent parts: In the first part, we derive a criterion to determine when a translationally invariant Matrix Product State (MPS) has long range localizable entanglement, which indicates that the…
Symmetries are important guiding principle for phase transitions. We systematically construct field theory models with local quantum fields that exhibit the following phase transitions: (1) different symmetry protected topological (SPT)…
A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of the system which are…
It is well-known that point-set topology (without additional structure) lacks the capacity to generalize the analytic concepts of completeness, boundedness, and other typically-metric properties. The ability of metric spaces to capture this…
We propose a way -- universal wave function overlap -- to extract universal topological data from generic ground states of gapped systems in any dimensions. Those extracted topological data should fully characterize the topological orders…
A set of new exact ground states of the generalized Hubbard models in arbitrary dimensions with explicitly given parameter regions is presented. This is based on a simple method for constructing exact ground states for homogeneous quantum…
Measurement-based quantum computing is a promising paradigm of quantum computation, where universal computing is achieved through a sequence of local measurements. The backbone of this approach is the preparation of multipartite…
High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and…
The orbifold construction via topological defects in quantum field theory can either be understood as a state sum construction internal to a given ambient theory, or as the procedure of (identifying and) gauging ordinary and…
Our work aims to introduce generalization of soft $ \mu $-compact soft generalized topological spaces, namely; soft nearly $ \mu $-compact spaces which are defined over initial universe with a fixed set of parameters. Basic properties and…
Behaviors of many engineering systems are described by lumped parameter models that encapsulate the spatially distributed nature of the system into networks of lumped elements; the dynamics of such a network is governed by a system of…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…