Related papers: Superposed Random Spin Tensor Networks and their H…
We present a continuous tensor-network construction for the states of quantum fields called cPEPS (continuous projected entangled pair state), which enjoys the same spatial and global symmetries of ground-states of relativistic field…
Hierarchical networks are attracting a renewal interest for modelling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean-field limitations. Here we consider the…
We propose a new example of discrete holography that provides a new step towards establishing the AdS/CFT duality for discrete spaces. A class of boundary Hamiltonians is obtained in a natural way from regular tilings of the hyperbolic…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a…
Projected entangled pair states (PEPS) on finite two-dimensional lattices are a natural ansatz for representing ground states of local many-body Hamiltonians, as they inherently satisfy the boundary law of entanglement entropy. In this…
We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two…
Complex networks are characterized by several topological properties: degree distribution, clustering coefficient, average shortest path length, etc. Using a simple model to generate scale-free networks embedded on geographical space, we…
First principle network models are crucial to make sense of the intricate topology of real complex networks. While modeling efforts have been quite successful in undirected networks, generative models for networks with asymmetric…
In continuous quantum field theories, the entanglement entropy of a subsystem with sharp corners on its boundary exhibits a universal corner-dependent contribution. We study this contribution through the lens of lattice discretization, and…
We introduce a unifying framework for the construction of holographic tensor networks, based on the theory of hyperbolic buildings. The underlying dualities relate a bulk space to a boundary which can be homeomorphic to a sphere, but also…
Symmetry is usually defined via transformations described by a (higher) group. But a symmetry really corresponds to an algebra of local symmetric operators, which directly constrains the properties of the system. In this paper, we point out…
We describe a simple and yet surprisingly powerful probabilistic technique which shows how to find in a dense graph a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently this technique…
We study a topological field theory in four dimensions on a manifold with boundary. A bulk-boundary interaction is introduced through a novel variational principle rather than explicitly. Through this scheme we find that the boundary values…
We study the quantum statistical electronic properties of random networks which inherently lack a fixed spatial dimension. We use tools like the density of states (DOS) and the inverse participation ratio(IPR) to uncover various phenomena,…
We propose a single-layer tensor network framework for the variational determination of ground states in two-dimensional quantum lattice models. By combining the nested tensor network method [Phys. Rev. B 96, 045128 (2017)] with the…
Atom manipulation by scanning tunneling microscopy was used to construct quantum dots on the InAs(111)A surface. Each dot comprised six ionized indium adatoms. The positively charged adatoms create a confining potential acting on…
We compute the entropy of a closed bounded region of space for pure 3d Riemannian gravity formulated as a topological BF theory for the gauge group SU(2) and show its holographic behavior. More precisely, we consider a fixed graph embedded…
Tensor networks are a powerful formalism for transforming one set of degrees of freedom to another. They have been heavily used in analyzing the geometry of bulk/boundary correspondence in conformal field theories. Here we develop a…
Recent work has shown that for one-dimensional quantum states that can be effectively approximated by matrix product operators (MPOs), a polynomial number of copies of the state suffices for reconstruction. Compared to MPOs in one…