Related papers: Measuring Topological Order
We study the topological characterization of the energy gaps in general two-dimensional quasiperiodic systems consisting of multiple periodicities, represented by twisted two-dimensional materials. We show that every single gap is uniquely…
Topology is central to understanding and engineering materials that display robust physical phenomena immune to imperfections. Different topological phases of matter are characterised by topological invariants. In energy-conserving…
Soliton molecules, bound states of two solitons, can be important for the informatics using solitons and the quest for exotic particles in a wide range of physical systems from unconventional superconductors to nuclear matter and Higgs…
We theoretically introduce a quasi-1D magnetic heterostructure of alternating 2D topological and normal insulator strips. Its low-energy physics is governed by a hybrid Hamiltonian intertwining the Su-Schrieffer-Heeger and Shockley models,…
We develop a family of chiral measures to quantify the chirality of a distribution and assign it a handedness. Our measures are built using the tensorial moments of the distribution, which naturally encode its spatial character, not only…
We use a 2-categorical version of (de-)equivariantization to classify (3+1)d topological orders with a finite $G$-symmetry. In particular, we argue that (3+1)d fermionic topological order with $G$-symmetry correspond to…
Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant…
Octupolar order is described in two space dimensions in terms of the maxima (and conjugated minima) of the probability density associated with a third-rank, fully symmetric and traceless tensor. Such a representation is shown to be…
Topological states of matter exhibit many novel properties due to the presence of robust topological invariants such as the Chern index. These global characteristics pertain to the system as a whole and are not locally defined. However,…
We theoretically examine the use of a statistical distance measure, the indistinguishability, as a generic tool for the identification of topological order. We apply this measure to the toric code and two fractional quantum Hall models. We…
In this short paper, we argue that the chiral central charge $c_-$ of a (2+1)d topological ordered state is sometimes strongly constrained by 't Hooft anomaly of anti-unitary global symmetry. For example, if a (2+1)d fermionic TQFT has a…
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…
We define a new topological invariant of line arrangements in the complex projective plane. This invariant is a root of unity defined under some combinatorial restrictions for arrangements endowed with some special torsion character on the…
We present the first examples of topological phases of matter with uniform power for measurement-based quantum computation. This is possible thanks to a new framework for analyzing the computational properties of phases of matter that is…
Topological insulators are substances which are bulk insulators but which carry current via special "topologically protected" edge states. The understanding of long range topological order in these systems is built around the idea of a…
Given a microscopic lattice Hamiltonian for a topologically ordered phase, we describe a tensor network approach to characterize its emergent anyon model and, in a chiral phase, also its gapless edge theory. First, a tensor network…
The relation between thermodynamic phase transitions in classical systems and topological changes in their configuration space is discussed for two physical models and contains the first exact analytic computation of a topologic invariant…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
The non-Abelian geometric phases of the robust degenerate ground states were proposed as physically measurable defining properties of topological order in 1990. In this paper we discuss in detail such a quantitative characterization of…
Topological phases are characterised by a topological invariant that remains unchanged by deformations in the Hamiltonian. Materials exhibiting topological phases include topological insulators, superconductors exhibiting strong spin-orbit…