Breakdown of quasilocality in long-range quantum lattice models

TL;DR

This paper investigates how long-range interactions in quantum lattice models affect the spread of correlations, revealing conditions where causality is broken and correlations propagate faster than traditional bounds suggest.

Contribution

It establishes the necessity and sufficiency of decay conditions for correlation spreading and demonstrates the breakdown of causal regions in long-range quantum models.

Findings

Correlation spreading is limited by a Lieb-Robinson-type bound for certain exponents.

Causal regions disappear and correlations become distance-independent for smaller exponents.

Numerical simulations show a transition from sound cone to supersonic propagation as the decay exponent varies.

Abstract

We study the non-equilibrium dynamics of correlations in quantum lattice models in the presence of long-range interactions decaying asymptotically as a power law. For exponents larger than the lattice dimensionality, a Lieb-Robinson-type bound effectively restricts the spreading of correlations to a causal region, but allows supersonic propagation. We show that this decay is not only sufficient but also necessary. Using tools of quantum metrology, for any exponents smaller than the lattice dimension, we construct Hamiltonians giving rise to quantum channels with capacities not restricted to a causal region. An analytical analysis of long-range Ising models illustrates the disappearance of the causal region and the creation of correlations becoming distance-independent. Numerical results obtained using matrix product state methods for the XXZ spin chain reveal the presence of a sound cone for large exponents, and supersonic propagation for small ones. In all models we analyzed the fast spreading of correlations follows a power law, but not the exponential increase of the long-range Lieb-Robinson bound.