Related papers: Nested Topological Order
We study the connection between topological order and degeneracy of the singular value spectrum by explicitly solving the two-dimensional dimerized quantum Heisenberg model in the form of tensor product state ansatz. Based on the ground…
We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry protected topological states can be…
Topological phases support edge states that can be robust to material deformations and other perturbations. While well-studied in quantum systems, topological phases have also been observed in stochastic and biochemical systems, yet it…
Coexistence of various ordered chaotic states in a Hamiltonian system is studied with the use of a symplectic coupled map lattice. Besides the clustered states for the attractive interaction, a novel chaotic ordered state is found for a…
Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks…
Motivated by experimental progress in the growth of heavy transition metal oxides, we theoretically study a class of lattice models of interacting fermions with strong spin-orbit coupling. Focusing on interactions of intermediate strength,…
In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that…
In this paper we explore how non trivial boundary conditions could influence the entanglement entropy in a topological order in 2+1 dimensions. Specifically we consider the special class of topological orders describable by the quantum…
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…
There are indications from the large-N analysis that multi-channel Kondo lattices have topological order. We use the coupled-wire construction to study the channel paramagnetic regime of a two-channel Kondo lattice model of spin-1/2 SU(2)…
Recently, the search for topological states of matter has turned to non-Hermitian systems, which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices modeled through non-Hermitian Hamiltonians appear in the…
We argue, based on general principles, that topological order is essential to realize fractionalization in gapped insulating phases in dimensions $d \geq 2$. In $d=2$ with genus $g$, we derive the existence of the minimum topological…
We propose a general framework for studying two-dimensional (2D) topologically ordered states subject to local correlated errors and show that the resulting mixed-state can display intrinsically mixed-state topological order (imTO) --…
I discuss a family of statistical-mechanics models in which (some classes of) elements of a finite group $G$ occupy the (directed) edges of a lattice; the product around any plaquette is constrained to be the group identity $e$. Such a…
The phenomenon of degeneracy of an $N-$plet of bound states is studied in the framework of quantum theory of closed (i.e., unitary) systems. For an underlying Hamiltonian $H=H(\lambda)$ the degeneracy occurs at a Kato's exceptional point…
Nematic phases, breaking spontaneously rotational symmetry, provide for ubiquitously observed states of matter in both classical and quantum systems. These nematic states may be further classified by their $N$--fold rotational invariance…
This work focuses on steady and unsteady Navier-Stokes equations in a reduced order modeling framework. The methodology proposed is based on a Proper Orthogonal Decomposition within a levelset geometry description and the problems of…
Topological orders can be used as media for topological quantum computing --- a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing…
We theoretically analyze the depletion dynamics of an ensemble of cold atoms in a quasi one-dimensional optical lattice where atoms in one of the lattice sites are subject to decay. Unlike the previous studies of this problem in R.…
Some popular mechanisms for restricting the diffusion of waves include introducing disorder (to provoke Anderson localization) and engineering topologically non-trivial phases (to allow for topological edge states to form). However, other…