Breakdown of quasilocality in long-range quantum lattice models.
We study the nonequilibrium dynamics of correlations in quantum lattice models in the presence of long-range interactions decaying asymptotically as a power law. For exponents larger than the lattice dimensionality, a Lieb-Robinson-type bound effectively restricts the spreading of correlations to a causal region, but allows supersonic propagation. We show that this decay is not only sufficient but also necessary. Using tools of quantum metrology, for any exponents smaller than the lattice dimension, we construct Hamiltonians giving rise to quantum channels with capacities not restricted to a causal region. An analytical analysis of long-range Ising models illustrates the disappearance of the causal region and the creation of correlations becoming distance independent. Numerical results obtained using matrix product state methods for the XXZ spin chain reveal the presence of a sound cone for large exponents and supersonic propagation for small ones. In all models we analyzed, the fast spreading of correlations follows a power law, but not the exponential increase of the long-range Lieb-Robinson bound.
Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.
Jens
J
Eisert
Institute of Theoretical Physics, University of Stellenbosch, Stellenbosch 7600, South Africa and National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa.
Mauritz
M
van den Worm
Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany.
Salvatore R
SR
Manmana
Institute of Theoretical Physics, University of Stellenbosch, Stellenbosch 7600, South Africa and National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa.
Michael
M
Kastner