Different modes of motion in special translationally invariant many-body systems

P. Möbius

Wojciech De Roeck, François Huveneers

Cheng-Li Wu

Marko Žnidarič

We study Ruelle-Pollicott resonances in translationally invariant quantum many-body lattice systems via spectra of a momentum-resolved operator propagator on infinite systems. Momentum dependence gives insight into the decay of correlation functions, showing that, depending on their symmetries, different correlation functions in general decay with different rates. Focusing on the kicked Ising model, the spectrum seems to be typically composed of an annular random matrix-like ring whose size we theoretically predict, and few isolated resonances. We identify several interesting regimes, including a mixing regime with a power-law decay of correlation functions. In that regime, we also observe a huge difference in timescales of different correlation functions due to an almost conserved operator. An exact expression for the singular values of the operator propagator is conjectured, showing that it becomes singular at a special point.

J Tura, A B Sainz, T Vértesi +3 more

Bell inequalities are natural tools that allow one to certify the presence of nonlocality in quantum systems. The known constructions of multipartite Bell inequalities contain, however, correlation functions involving all observers, making their experimental implementation difficult. The main purpose of this work is to explore the possibility of witnessing nonlocality in multipartite quantum states from the easiest-to-measure quantities, that is, the two-body correlations. In particular, we determine all three- and four-partite Bell inequalities constructed from one- and two-body expectation values that obey translational symmetry, and show that they reveal nonlocality in multipartite states. Also, by providing a particular example of a five-partite Bell inequality, we show that nonlocality can be detected from two-body correlators involving only nearest neighbours. Finally, we demonstrate that any translationally invariant Bell inequality can be maximally violated by a translationally invariant state and the same set of observables at all sites. We provide a numerical algorithm allowing one to seek for maximal violation of a translationally invariant Bell inequality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.

Yevgeny Bar Lev, David R. Reichman