Dynamics of quantum many-body systems with long-range interactions

Léa Ferreira dos Santos, Francisco Pérez-Bernal

Tomotaka Kuwahara

The dynamics of quantum systems strongly depends on the local structure of the Hamiltonian. For short-range interacting systems, the well-known Lieb–Robinson bound defines the effective light cone with an exponentially small error with respect to the spatial distance, whereas we can obtain only polynomially small errors for distance in long-range interacting systems. In this paper, we derive a qualitatively new bound for quantum dynamics by considering how many spins can correlate with each other after time evolution. Our bound characterizes the number of spins which support the many-body entanglement with exponentially small errors and is valid for a large class of Hamiltonians including long-range interacting systems. To demonstrate the advantage of our approach in quantum many-body systems, we apply our bound to prove several fundamental properties which have not been derived from the Lieb–Robinson bound.

Alexey Vyacheslavovich Gorshkov

Dominik Sulz, Christian Lubich, Gianluca Ceruti +2 more

Open quantum systems provide a conceptually simple setting for the exploration of collective behavior stemming from the competition between quantum effects, many-body interactions, and dissipative processes. They may display dynamics distinct from that of closed quantum systems or undergo nonequilibrium phase transitions which are not possible in classical settings. However, studying open quantum many-body dynamics is challenging, in particular, in the presence of critical long-range correlations or long-range interactions. Here, we make progress in this direction and introduce a numerical method for open quantum systems, based on tree tensor networks. Such a structure is expected to improve the encoding of many-body correlations and we adopt an integration scheme suited for long-range interactions and applications to dissipative dynamics. We test the method using a dissipative Ising model with power-law decaying interactions and observe signatures of a first-order phase transition for power-law exponents smaller than 1.

Marco Távora, Jonathan Torres-Herrera, Léa Ferreira dos Santos

Lorenzo Cevolani, Julien Despres, Giuseppe Carleo +2 more

The ability of many-body systems to spread out information has fundamental impact on quantum information, thermodynamics, and transport dynamics. Long-range interactions are particularly appealing as they pave the way to nonballistic dynamics, and recent observations challenge existing bounds. Here, the authors develop a general theory based on quasiparticles that unifies short-range and long-range systems. They show that, in general, two signals coexist and carry complementary information about the many-body spectrum. One of the signals is subballistic while the other may be superballistic. This result has fundamental implications on the interpretation of experiments and offers tools to probe many-body systems.