Despite extensive research on long-range interacting quantum systems, the physical mechanism responsible for the emergence of light cones remains unidentified. This work presents a novel perspective on the origins of locality and emergent light cones in quantum systems with long-range interactions. We identify a mechanism in such spin chains where effective entanglement light cones emerge due to destructive interference among quantum effects that entangle spins. Although long-range entangling effects reach beyond the identified light cone, due to destructive interference, entanglement remains exponentially suppressed in that region, ultimately leading to the formation of the light cone. We demonstrate that this interference not only drives but is also necessary for the emergence of light cones. Furthermore, our analysis reveals that reducing the interaction range weakens this interference, surprisingly increasing the speed of entanglement transport, an effect that opens new experimental opportunities for investigation.
Despite extensive research on long-range interacting quantum systems, the physical mechanism responsible for the emergence of light cones remains unidentified. This work presents a novel perspective on the origins of locality and emergent light cones in quantum systems with long-range interactions. We identify a mechanism in such spin chains where effective entanglement light cones emerge due to destructive interference among quantum effects that entangle spins. Although long-range entangling effects reach beyond the identified light cone, due to destructive interference, entanglement remains exponentially suppressed in that region, ultimately leading to the formation of the light cone. We demonstrate that this interference not only drives but is also necessary for the emergence of light cones. Furthermore, our analysis reveals that reducing the interaction range weakens this interference, surprisingly increasing the speed of entanglement transport, an effect that opens new experimental opportunities for investigation.
Abstract In this paper, we revisit a “relatively local” model proposed in [1], where locality and dimensionality of space only emerges from the entanglement structure of the state the system is in. Various quantities such as butterfly velocity/entanglement speed can be defined similarly, at least in the regime where locality is well defined and a light cone structure emerges in the correlation between sites. We find that the relations observed between them in local models [2] are not respected. In particular, we conjecture that the hierarchy of the interaction over different distances provides different “layers” of light cones. When long range interactions are sufficiently suppressed, the effective light cones are dominated by linear behaviour with little remnant of non-locality. This could potentially be used as a physical smoking gun for emergent locality in non-local models.
In nonrelativistic quantum theories with short-range Hamiltonians, a velocity v can be chosen such that the influence of any local perturbation is approximately confined to within a distance r until a time $t\ensuremath{\sim}r/v$, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law ($1/{r}^{\ensuremath{\alpha}}$) interactions, when $\ensuremath{\alpha}$ exceeds the dimension D, an analogous bound confines influences to within a distance r only until a time $t\ensuremath{\sim}(\ensuremath{\alpha}/v)\mathrm{log}r$, suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time. We rule out this possibility; light cones of power-law interacting systems are bounded by a polynomial for $\ensuremath{\alpha}>2D$ and become linear as $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\infty}$. Our results impose strong new constraints on the growth of correlations and the production of entangled states in a variety of rapidly emerging, long-range interacting atomic, molecular, and optical systems.
Understanding how information spreads in non-relativistic many-body systems is a central issue for quantum information processing. While short-range interactions confine information within a local light cone, long-range interactions typically lead to uncontrolled nonlocal spread across the entire system. Here, we demonstrate that this apparent dichotomy is not fundamental and that nonlocality in systems with long-range interactions can be deterministically controlled. By mapping spin dynamics to a hard-core boson chain, we identify a regime in which the causal space-time landscape can be precisely shaped. We show that placing spin excitations in a polarized background allows a local perturbation to trigger nonlocal signals exactly at the positions of these excitations. These pre-selected sites act as seeds for new, effective light cones, allowing information to bypass the bulk and re-emerge at distant, programmable locations. This mechanism avoids uncontrollable global nonlocality while circumventing the speed limits associated with local transport. By engineering these nonlocal communication channels, our findings offer a versatile framework for information distribution relevant to quantum memories, error correction, and programmable platforms such as trapped ions.
Locality imposes stringent constraints on the spreading of information in nonrelativistic quantum systems, which is reminiscent of a ``light cone,'' a causal structure arising in their relativistic counterparts. Long-range interactions can potentially soften such constraints, allowing almost instantaneous long jumps of particles, into the ``spacelike'' region, thus defying causality. Since interactions decaying as a power law with distance ${r}^{\ensuremath{-}\ensuremath{\alpha}}$ are ubiquitous in nature, it is pertinent to understand what is the fate of causality and information spreading in such systems. Using a numerically exact technique we address these questions by studying the out-of-time-order correlation function of a representative generic system in one dimension. We show that while the interactions are long range, their effect on information spreading is asymptotically negligible as long as $\ensuremath{\alpha}>1$. In this range we find a complex compound behavior, where, after a short transient, a fully local behavior emerges, yielding asymptotic light cones virtually indistinguishable from light cones in corresponding local models. The long-range nature of the interaction is only expressed in the power-law leaking of information from the light cone, with the same exponent as the exponent of the interaction $\ensuremath{\alpha}$. Our results directly apply also to corresponding response functions and suggest that previously obtained rigorous bounds on information spreading in long-range interacting systems are not tight, and could be potentially improved.
It is well known that the notions of spatial locality are often lost in quantum systems with long-range interactions, as exhibited by the emergence of phases with exotic long-range order and faster propagation of quantum correlations. We demonstrate here that such induced ``quasinonlocal'' effects do not necessarily translate to growth of global entanglement in the quantum system. By investigating the ground and quenched states of the variable-range, spin-1/2 Heisenberg Hamiltonian, we observe that the genuine multiparty entanglement in the system can either increase or counterintuitively diminish with a growing range of interactions. The behavior is reflective of the underlying phase structure of the quantum system and provides key insights for generation of multipartite entanglement in experimental atomic, molecular, and optical physics where such variable-range interactions have been implemented.
Enhanced experimental capabilities to control nonlocal and power-law decaying interactions are currently fueling intense research in the domain of quantum many-body physics. Compared to their counterparts with short-ranged interactions, long-range interacting systems display novel physics, such as nonlinear light cones for the propagation of information or inequivalent thermodynamic ensembles. In this work, we consider generic long-range open quantum systems in arbitrary dimensions and focus on the so-called strong long-range regime. We prove that in the thermodynamic limit local properties, captured by reduced quantum states, are described by an emergent noninteracting theory. Here, the dynamics factorizes and the individual constituents of the system evolve independently such that no correlations are generated over time. In this sense, long-range interacting systems are locally noninteracting. This has significant implications for their relaxation behavior, for instance, in relation to the emergence of long-lived quasistationary states or to the absence of thermalization.