Emergent entanglement structures and self-similarity in quantum spin chains

• URL: http://arxiv.org/abs/2007.06989v1
• Date: Tue, 14 Jul 2020 12:13:29 GMT
• Title: Emergent entanglement structures and self-similarity in quantum spin chains
• Authors: Boris Sokolov, Matteo A. C. Rossi, Guillermo Garc\'ia-P\'erez and Sabrina Maniscalco
• Abstract summary: We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin chain model, the XX model, and showing that it brings to light new phenomena.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin chain model, the XX model, and showing that it brings to light new phenomena. The analysis of these entanglement networks reveals that the gradual establishment of quasi-long range order is accompanied by a symmetry regarding single-spin concurrence distributions, as well as by instabilities in the network topology. Moreover, we identify the existence of emergent entanglement structures, spatially localised communities enforced by the global symmetry of the system that can be revealed by model-agnostic community detection algorithms. The network representation further unveils the existence of structural classes and a cyclic self-similarity in the state, which we conjecture to be intimately linked to the community structure. Our results demonstrate that the use of tools and concepts from complex network theory enables the discovery, understanding, and description of new physical phenomena even in models studied for decades.

Related papers

• A comprehensive exploration of interaction networks reveals a connection between entanglement and network structure [0.0]
  We investigate the connection between the structure of the interaction network and the eigenstate entanglement of the quantum Ising model.<n>Our results demonstrate that the minimum eigenstate entanglement of the quantum Ising model is governed by the specific structure of the interaction network.
  arXiv  Detail & Related papers  (2025-05-16T17:21:46Z)
• Unveiling hidden features of the Kitaev model through a complex-network analysis [0.9217021281095907]
  We introduce a density matrix-based network analysis to explore the ground state of the Kitaev chain. This approach successfully identifies the critical point associated with the topological phase transition and reveals a singular point where the ground state exhibits uniform, nonzero entanglement. We provide an analytical explanation for this singular behavior and establish a connection to the concept of ground state factorization observed in spin chains.
  arXiv  Detail & Related papers  (2025-05-01T10:37:46Z)
• Local models and Bell inequalities for the minimal triangle network [84.67234803583032]
  Nonlocal correlations enable surprising phenomena in quantum information and quantum foundations. We study one of the simplest scenarios, namely that of distributions invariant under permutations of parties in the minimal triangle network. We provide new insights on the existence of a classical-quantum gap in the triangle network with binary outcomes.
  arXiv  Detail & Related papers  (2025-03-20T19:11:06Z)
• Clustering-induced localization of quantum walks on networks [0.0]
  Quantum walks on networks are a paradigmatic model in quantum information theory. We show how localization emerges in highly clustered networks by attaching triangles. We then show that localization also occurs in Kleinberg small-world networks and Holme--Kim power-law cluster networks.
  arXiv  Detail & Related papers  (2024-12-05T16:40:57Z)
• Compositional Structures in Neural Embedding and Interaction Decompositions [101.40245125955306]
  We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks. We introduce a characterization of compositional structures in terms of "interaction decompositions" We establish necessary and sufficient conditions for the presence of such structures within the representations of a model.
  arXiv  Detail & Related papers  (2024-07-12T02:39:50Z)
• Uncovering the hidden core-periphery structure in hyperbolic networks [0.0]
  hyperbolic network models exhibit fundamental and essential features, like small-worldness, scale-freeness, high-clustering coefficient, and community structure. In this paper, we explore the presence of an important feature, the core-periphery structure, in the hyperbolic network models.
  arXiv  Detail & Related papers  (2024-06-28T14:39:21Z)
• Quantum-Inspired Analysis of Neural Network Vulnerabilities: The Role of Conjugate Variables in System Attacks [54.565579874913816]
  Neural networks demonstrate inherent vulnerability to small, non-random perturbations, emerging as adversarial attacks. A mathematical congruence manifests between this mechanism and the quantum physics' uncertainty principle, casting light on a hitherto unanticipated interdisciplinarity.
  arXiv  Detail & Related papers  (2024-02-16T02:11:27Z)
• Imaginary components of out-of-time correlators and information scrambling for navigating the learning landscape of a quantum machine learning model [0.0]
  We analytically illustrate that hitherto unexplored imaginary components of out-of-time correlators can provide unprecedented insight into the information scrambling capacity of a graph neural network. Such an analysis demystifies the training of quantum machine learning models by unraveling how quantum information is scrambled through such a network.
  arXiv  Detail & Related papers  (2022-08-29T06:17:28Z)
• Signed Network Embedding with Application to Simultaneous Detection of Communities and Anomalies [25.541992448747695]
  This paper develops a unified embedding model for signed networks to disentangle the intertwined balance structure and anomaly effect. The proposed model captures both balance structure and anomaly effect through a low rank plus sparse matrix decomposition. The advantage of the proposed embedding model is also demonstrated through extensive numerical experiments on both synthetic networks and an international relation network.
  arXiv  Detail & Related papers  (2022-07-08T03:58:56Z)
• Distribution of Gaussian Entanglement in Linear Optical Systems [0.0]
  Entanglement is an essential ingredient for building a quantum network that can have many applications. We study the conservation and distribution of Gaussian entanglement in a linear network using a new quantifier for bipartite entanglement.
  arXiv  Detail & Related papers  (2021-05-27T20:34:54Z)
• Full network nonlocality [68.8204255655161]
  We introduce the concept of full network nonlocality, which describes correlations that necessitate all links in a network to distribute nonlocal resources. We show that the most well-known network Bell test does not witness full network nonlocality. More generally, we point out that established methods for analysing local and theory-independent correlations in networks can be combined in order to deduce sufficient conditions for full network nonlocality.
  arXiv  Detail & Related papers  (2021-05-19T18:00:02Z)
• Localisation in quasiperiodic chains: a theory based on convergence of local propagators [68.8204255655161]
  We present a theory of localisation in quasiperiodic chains with nearest-neighbour hoppings, based on the convergence of local propagators. Analysing the convergence of these continued fractions, localisation or its absence can be determined, yielding in turn the critical points and mobility edges. Results are exemplified by analysing the theory for three quasiperiodic models covering a range of behaviour.
  arXiv  Detail & Related papers  (2021-02-18T16:19:52Z)
• Emergent complex quantum networks in continuous-variables non-Gaussian states [0.0]
  We study a class of continuous-variable quantum states that present both multipartite entanglement and non-Gaussian statistics. In particular, the states are built from an initial imprinted cluster state created via Gaussian entangling operations.
  arXiv  Detail & Related papers  (2020-12-31T13:58:37Z)
• A Chain Graph Interpretation of Real-World Neural Networks [58.78692706974121]
  We propose an alternative interpretation that identifies NNs as chain graphs (CGs) and feed-forward as an approximate inference procedure. The CG interpretation specifies the nature of each NN component within the rich theoretical framework of probabilistic graphical models. We demonstrate with concrete examples that the CG interpretation can provide novel theoretical support and insights for various NN techniques.
  arXiv  Detail & Related papers  (2020-06-30T14:46:08Z)
• Entanglement Classification via Neural Network Quantum States [58.720142291102135]
  In this paper we combine machine-learning tools and the theory of quantum entanglement to perform entanglement classification for multipartite qubit systems in pure states. We use a parameterisation of quantum systems using artificial neural networks in a restricted Boltzmann machine (RBM) architecture, known as Neural Network Quantum States (NNS)
  arXiv  Detail & Related papers  (2019-12-31T07:40:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.