Speed limits on quantum dynamics with long-range interactions

Tan Van Vu, Tomotaka Kuwahara, Keiji Saito

Understanding the ultimate rate at which information propagates is a pivotal issue in nonequilibrium physics. Nevertheless, the task of elucidating the propagation speed inherent in quantum bosonic systems presents challenges due to the unbounded nature of their interactions. In this study, we tackle the problem of macroscopic particle transport in a long-range generalization of the lattice Bose-Hubbard model through the lens of the quantum speed limit. By developing a unified approach based on optimal transport theory, we rigorously prove that the minimum time required for macroscopic particle transport is always bounded by the distance between the source and target regions, while retaining its significance even in the thermodynamic limit. Furthermore, we derive an upper bound for the probability of observing a specific number of bosons inside the target region, thereby providing additional insights into the dynamics of particle transport. Our results hold true for arbitrary initial states under both long-range hopping and long-range interactions, thus resolving an open problem of particle transport in generic bosonic systems.

Alexey Vyacheslavovich Gorshkov

Lorenzo Cevolani, Giuseppe Carleo, Laurent Sanchez-Palencia

We study the out-of-equilibrium dynamics of quantum systems with long-range interactions. Two different models describing, respectively, interacting lattice bosons and spins are considered. Our study relies on a combined approach based on accurate many-body numerical calculations as well as on a quasiparticle microscopic theory. For sufficiently fast decaying long-range potentials, we find that the quantum speed limit set by the long-range Lieb-Robinson bounds is never attained and a purely ballistic behavior is found. For slowly decaying potentials, a radically different scenario is observed. In the bosonic case, a remarkable local spreading of correlations is still observed, despite the existence of infinitely fast traveling excitations in the system. This is in marked contrast to the spin case, where locality is broken. We finally provide a microscopic justification of the different regimes observed and of the origin of the protected locality in the bosonic model.

Antti Knowles

Thomás Fogarty, Sebastian Deffner, Thomas Busch +1 more

A remarkable feature of quantum many-body systems is the orthogonality catastrophe that describes their extensively growing sensitivity to local perturbations and plays an important role in condensed matter physics. Here we show that the dynamics of the orthogonality catastrophe can be fully characterized by the quantum speed limit and, more specifically, that any quenched quantum many-body system, whose variance in ground state energy scales with the system size, exhibits the orthogonality catastrophe. Our rigorous findings are demonstrated by two paradigmatic classes of many-body systems-the trapped Fermi gas and the long-range interacting Lipkin-Meshkov-Glick spin model.

Léa Ferreira dos Santos, Francisco Pérez-Bernal