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      Stripe order in the underdoped region of the two-dimensional Hubbard model

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          Charged magnetic domain lines and the magnetism of high-Tcoxides

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            Is Open Access

            Area laws for the entanglement entropy - a review

            Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: The entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such "area laws" for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum many-body physics where they have important implications on the numerical simulation of lattice models. In this Colloquium we review the current status of area laws in these fields. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation, and disordered systems, non-equilibrium situations, classical correlation concepts, and topological entanglement entropies are discussed. A significant proportion of the article is devoted to the quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. We discuss matrix-product states, higher-dimensional analogues, and states from entanglement renormalization and conclude by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations.
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              Complexity in Strongly Correlated Electronic Systems

              A wide variety of experimental results and theoretical investigations in recent years have convincingly demonstrated that several transition metal oxides and other materials, have dominant states that are not spatially homogeneous. This occurs in cases in which several physical interactions -- spin, charge, lattice, and/or orbital -- are simultaneously active. This phenomenon causes interesting effects, such as colossal magnetoresistance, and it also appears crucial to understand the high temperature superconductors. The spontaneous emergence of electronic nanometer-scale structures in transition metal oxides, and the existence of many competing states, are properties often associated with complex matter where nonlinearities dominate, such as soft materials and biological systems. This electronic complexity could have potential consequences for applications of correlated electronic materials, because not only charge (semiconducting electronic), or charge and spin (spintronics) are of relevance, but in addition the lattice and orbital degrees of freedom are active, leading to giant responses to small perturbations. Moreover, several metallic and insulating phases compete, increasing the potential for novel behavior.
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                Author and article information

                Journal
                Science
                Science
                American Association for the Advancement of Science (AAAS)
                0036-8075
                1095-9203
                November 30 2017
                December 01 2017
                : 358
                : 6367
                : 1155-1160
                Article
                10.1126/science.aam7127
                29191901
                a3f922c9-b9f6-4eed-9233-5892ac0fbd4c
                © 2017

                http://www.sciencemag.org/about/science-licenses-journal-article-reuse

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