Entanglement and fluctuations in the XXZ model with power-law interactions

We investigate the ground-state properties of the spin-1/2 XXZ model with power-law-decaying (1/r(alpha)) interactions, which describe spins interacting with long-range transverse (XX) ferromagnetic interactions and longitudinal (Z) antiferromagnetic interactions, or hard-core bosons with long-range repulsion and hopping. The long-range nature of the couplings allows us to quantitatively study the spectral, correlation, and entanglement properties of the system by making use of linear spin-wave theory, supplemented with density-matrix renormalization group in one-dimensional systems. Our most important prediction is the existence of three distinct coupling regimes, depending on the decay exponent a and number of dimensions d: (1) a short-range regime for a > d + sigma(c) (where sigma(c) = 1 in the gapped Neel antiferromagnetic phase exhibited by the XXZ model, and sigma(c) = 2 in the gapless XY ferromagnetic phase), sharing the same properties as those of finite-range interactions (alpha =8); (2) a long-range regime alpha < d, sharing the same properties as those of the infinite-range interactions (alpha = 0) in the thermodynamic limit; and (3) a most intriguing medium-range regime for d < a < d + sc, continuously interpolating between the finite-range and the infinite-range behavior. The latter regime is characterized by elementary excitations with a long-wavelength dispersion relation. omega approximate to Delta(g) + ck(z) in the gapped phase, and. omega similar to k(z) in the gapless phase, exhibiting a continuously varying dynamical exponent z = (alpha - d)/sigma(c). In the gapless phase of the model the z exponent is found to control the scaling of fluctuations, the decay of correlations, and a universal subdominant term in the entanglement entropy, leading to a very rich palette of behaviors for ground-state quantum correlations beyond what is known for finite-range interactions.