Treelike interactions and fast scrambling with cold atoms

Bentsen, Gregory and Hashizume, Tomohiro and Buyskikh, Anton S. and Davis, Emily J. and Daley, Andrew J. and Gubser, Steven S. and Schleier-Smith, Monika (2019) Treelike interactions and fast scrambling with cold atoms. Physical Review Letters, 123 (13). 130601. ISSN 1079-7114 (

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We propose an experimentally realizable quantum spin model that exhibits fast scrambling, based on nonlocal interactions that couple sites whose separation is a power of 2. By controlling the relative strengths of deterministic, nonrandom couplings, we can continuously tune from the linear geometry of a nearest-neighbor spin chain to an ultrametric geometry in which the effective distance between spins is governed by their positions on a tree graph. The transition in geometry can be observed in quench dynamics, and is furthermore manifest in calculations of the entanglement entropy. Between the linear and treelike regimes, we find a peak in entanglement and exponentially fast spreading of quantum information across the system. Our proposed implementation, harnessing photon-mediated interactions among cold atoms in an optical cavity, offers a test case for experimentally observing the emergent geometry of a quantum many-body system.