Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHaah codes on general three manifolds
122
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Haah codes represent a singularly interesting gapped Hamiltonian schema that has resisted a natural generalization, although recent work shows that the closely related type I fracton models are more commonplace. These type I siblings of Haah codes are better understood, and a generalized topological quantum field theory framework has been proposed. Following the same conceptual framework, we outline a program to generalize Haah codes to all 3-manifolds using Hastings LR stabilizer codes for finite groups.
rate research
Read More
Entanglement renormalization group flow of the Haah cubic code produces another fracton model with 4 qubits per lattice site, dubbed as the Haah B-code. We provide a schema that generalizes both models to stabilizer codes on any finite group with 2q qubits per site and labeled by multi-subsets of the finite group and a symmetric binary matrix.
In this review article we describe the localization of three dimensional N=2 supersymmetric theories on compact manifolds, including the squashed sphere, S^3_b, the lens space, S^3_b/Z_p, and S^2 x S^1. We describe how to write supersymmetric actions on these spaces, and then compute the partition functions and other supersymmetric observables by employing the localization argument. We briefly survey some applications of these computations.
Fracton models, a collection of exotic gapped lattice Hamiltonians recently discovered in three spatial dimensions, contain some topological features: they support fractional bulk excitations (dubbed fractons), and a ground state degeneracy that is robust to local perturbations. However, because previous fracton models have only been defined and analyzed on a cubic lattice with periodic boundary conditions, it is unclear to what extent a notion of topology is applicable. In this paper, we demonstrate that the X-cube model, a prototypical type-I fracton model, can be defined on general three-dimensional manifolds. Our construction revolves around the notion of a singular compact total foliation of the spatial manifold, which constructs a lattice from intersecting stacks of parallel surfaces called leaves. We find that the ground state degeneracy depends on the topology of the leaves and the pattern of leaf intersections. We further show that such a dependence can be understood from a renormalization group transformation for the X-cube model, wherein the system size can be changed by adding or removing 2D layers of topological states. Our results lead to an improved definition of fracton phase and bring to the fore the topological nature of fracton orders.
Last years, bounds on the maximal quantum violation of general Bell inequalities were intensively discussed in the literature via different mathematical tools. In the present paper, we analyze quantum violation of general Bell inequalities via the LqHV (local quasi hidden variable) modelling framework, correctly reproducing the probabilistic description of every quantum correlation scenario. The LqHV mathematical framework allows us to derive for all d and N a new upper bound (2d-1)^{N-1} on the maximal violation by an N-qudit state of all general Bell inequalities, also, new upper bounds on the maximal violation by an N-qudit state of general Bell inequalities for S settings per site. These new upper bounds essentially improve all the known precise upper bounds on quantum violation of general multipartite Bell inequalities. For some S, d and N, the new upper bounds are attainable.
Three ways of constructing a non-Hermitian matrix with possible all real eigenvalues are discussed. They are PT symmetry, pseudo-Hermiticity, and generalized PT symmetry. Parameter counting is provided for each class. All three classes of matrices have more real parameters than a Hermitian matrix with the same dimension. The generalized PT-symmetric matrices are most general among the three. All self-adjoint matrices process a generalized PT symmetry. For a given matrix, it can be both PT-symmetric and P-pseudo-Hermitian with respect to some P operators. The relation between corresponding P and P operators is established. The Jordan block structures of each class are discussed. Explicit examples in 2x2 are shown.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
