Causality and quantum criticality in long-range lattice models

Article

关键词: POLAR-MOLECULES;    CRITICAL EXPONENTS;    SYSTEMS;    DIAMOND;    ENTANGLEMENT;    PROPAGATION;    DIMENSIONS;    TRANSITION;    SIMULATOR;    DYNAMICS;   

DOI  :  10.1103/PhysRevB.93.125128

来源: SCIE

【 摘 要 】

Long-range quantum lattice systems often exhibit drastically different behavior than their short-range counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent relativistic structure in the form of a light cone. Adopting a field-theoretic approach, we study the one-dimensional transverse-field Ising model with long-range interactions, and a fermionic model with long-range hopping and pairing terms, explore their critical and near-critical behavior, and characterize their response to local perturbations. We deduce the dynamic critical exponent, up to the two-loop order within the renormalization group theory, which we then use to characterize the emergent causal behavior. We show that beyond a critical value of the power-law exponent of the long-range couplings, the dynamics effectively becomes relativistic. Various other critical exponents describing correlations in the ground state, as well as deviations from a linear causal cone, are deduced for a wide range of the power-law exponent.

【 授权许可】

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