Quantum Order, Entanglement and Localization in Many-Body Systems

J. W. Clark, Hessam Habibian, Aikaterini Mandilara +1 more

Paul Cooney

Paper VI — Entanglement Information Locality and Many-Body Structure DescriptionThis work extends ordered-dynamics locality principles to composite systems, deriving entanglement structure and many-body correlations from operational constraints. Entanglement emerges as a necessary feature of jointly constrained information propagation, not as an added axiom. The paper clarifies the operational meaning of non-separability and establishes the foundations for multi-particle quantum structure within the ODRP. Keywordsentanglement; many-body systems; quantum correlations; operational locality; information theory; quantum foundations

S. M. Giampaolo, Beatrix C. Hiesmayr, Fabrizio Illuminati

Frustration in quantum many-body systems is quantified by the degree of incompatibility between the local and global orders associated, respectively, with the ground states of the local interaction terms and the global ground state of the total many-body Hamiltonian. This universal measure is bounded from below by the ground-state bipartite block entanglement. For many-body Hamiltonians that are sums of two-body interaction terms, a further inequality relates quantum frustration to the pairwise entanglement between the constituents of the local interaction terms. This additional bound is a consequence of the limits imposed by monogamy on entanglement shareability. We investigate the behavior of local pair frustration in quantum spin models with competing interactions on different length scales and show that valence bond solids associated with exact ground state dimerization correspond to a transition from generic frustration, i.e., geometric, common to classical and quantum systems alike, to genuine quantum frustration, i.e., solely due to the noncommutativity of the different local interaction terms. We discuss how such frustration transitions separating genuinely quantum orders from classical-like ones are detected by observable quantities such as the static structure factor and the interferometric visibility.

Anubhav Kumar Srivastava, Guillem Müller-Rigat, Maciej Lewenstein +1 more

S. M. Giampaolo, Beatrix C. Hiesmayr, Fabrizio Illuminati

Frustration in quantum many body systems is quantified by the degree of incompatibility between the local and global orders associated, respectively, to the ground states of the local interaction terms and the global ground state of the total many-body Hamiltonian. This universal measure is bounded from below by the ground-state bipartite block entanglement. For many-body Hamiltonians that are sums of two-body interaction terms, a further inequality relates quantum frustration to the pairwise entanglement between the constituents of the local interaction terms. This additional bound is a consequence of the limits imposed by monogamy on entanglement shareability. We investigate the behavior of local pair frustration in quantum spin models with competing interactions on different length scales and show that valence bond solids associated to exact ground-state dimerization correspond to a transition from generic frustration, i.e. geometric, common to classical and quantum systems alike, to genuine quantum frustration, i.e. solely due to the non-commutativity of the different local interaction terms. We discuss how such frustration transitions separating genuinely quantum orders from classical-like ones are detected by observable quantities such as the static structure factor and the interferometric visibility.

Frank Verstraete