Protected quasi-locality in quantum systems with long-range interactions

Lorenzo Cevolani (1) , Giuseppe Carleo (1) , Laurent Sanchez-Palencia (1)

1 Laboratoire Charles Fabry / Optique atomique

We study the out-of-equilibrium dynamics of quantum systems with long-range interactions. Two different models describing, respectively, lattice bosons, and spins are considered. Our study is based on a combined approach based, on one hand, on accurate many-body numerical calculations and, on the other hand, on a quasi-particle 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 with 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 bosonic models.

Mots clés: 0530Jp; 0270Ss; 0375Kk; 6785-d; 7510Pq

Domaines: Gaz Quantiques [cond-mat.quant-gas]; Electrons fortement corrélés [cond-mat.str-el]

Lorenzo Cevolani, Giuseppe Carleo, Laurent Sanchez-Palencia. Protected quasi-locality in quantum systems with long-range interactions. Physical Review A : Atomic, molecular, and optical physics [1990-2015], 2015, 92 (4), pp.041603. ⟨10.1103/PhysRevA.92.041603⟩. ⟨hal-01128147⟩