Related papers: Modular Matrices as Topological Order Parameter by…

In many applications, it is needed to change the topology of a tensor network directly and without approximation. This work will introduce a general scheme that satisfies these needs. We will describe the procedure by two examples and show…

Tensor networks are efficient factorisations of high-dimensional tensors into a network of lower-order tensors. They have been most commonly used to model entanglement in quantum many-body systems and more recently are witnessing increased…

Calculation of topological order parameters, such as the topological entropy and topological mutual information, are used to determine whether states possess topological order. Their calculation is expected to give reliable results when the…

This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network,…

Tensor networks are factorisations of high rank tensors into networks of lower rank tensors and have primarily been used to analyse quantum many-body problems. Tensor networks have seen a recent surge of interest in relation to supervised…

Topological phases are unique states of matter incorporating long-range quantum entanglement, hosting exotic excitations with fractional quantum statistics. We report a practical method to identify topological phases in arbitrary realistic…

The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering…

A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…

We introduce two-dimensional tensor network representations of finite groups carrying a 4-cocycle index. We characterize the associated gapped (2+1)D phases that emerge when these anomalous symmetries act on tensor network ground states. We…

We introduce a universally applicable method, based on the bond-algebraic theory of dualities, to search for generalized order parameters in disparate systems including non-Landau systems with topological order. A key notion that we advance…

Symmetry protected topological phases exhibit nontrivial short-ranged entanglement protected by symmetry and cannot be adiabatically connected to trivial product states while preserving the symmetry. In contrast, intrinsic topological…

Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and…

We introduce a general scheme for constructing order parameters (OPs) by extracting generic patterns from the dominant Fock states of many-body ground states. While topological phases are traditionally characterized by non-local invariants,…

We investigate a generalization of topological order from closed systems to open systems, for which the steady states take the place of ground states. We construct typical lattice models with steady-state topological order, and characterize…

Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…

A universal topological marker has been proposed recently to map the topological invariants of Dirac models in any dimension and symmetry class to lattice sites. Using this topological marker, we examine the conditions under which the…

The fields of entanglement theory and tensor networks have recently emerged as central tools for characterising quantum phases of matter. In this article, we determine the entanglement structure of ground states of gapped symmetric quantum…

We investigate topological properties of density matrices motivated by the question to what extent phenomena like topological insulators and superconductors can be generalized to mixed states in the framework of open quantum systems. The…

We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…