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a) The bound B(t) (black line) is approximately 4 times faster than the exact velocities (colored lines), for the case of a Heisenberg quantum spin chain with J = 1 meV and a length of 8 lattice sites. b) The bound B(t) (black line) for the physical interpretation is compared with the bounds˜B bounds˜ bounds˜B( P , t) (colored lines) which give a strictly mathematically related bound on the exact velocities. The interaction strengths of the modified Tersoff-Hamann model are chosen to be P = 4, 2, 1 and 0.5 meV.
Source publication
A Lieb-Robinson bound is a mathematical bound on velocities in quantum spin
systems, which is in analogy to the speed of light as maximum velocity in
relativity theory. An improved bound is derived and on a particular example it
is shown that this new bound is better by a factor of 100 than the original
bound. We also compare the improved bound wit...
Citations
Spin-polarized scanning tunneling microscopy is identified as a suitable
experimental technique to investigate the quantitative quality of
Lieb-Robinson bounds on the signal velocity. The latest, most general
bound is simplified and it is shown that there is a discrepancy by a
factor of approximately 4 between the corresponding limit speed and some
estimated exact velocities in atomic spin chains. The observed
discrepancy facilitates conclusions for a further mathematical
improvement of Lieb-Robinson bounds. The real signal propagation can be
modified with several experimental parameters from which the bounds are
independent. This enables the application of Lieb-Robinson bounds as
upper limits on the enhancement of the real signal speed for information
transport in spintronic devices.
We prove a general theorem which provides a strict lower bound on high-temperature Green-Kubo diffusion constants in locally interacting quantum lattice systems, under the assumption of existence of a quadratically extensive almost conserved quantity: an operator whose commutator with the lattice Hamiltonian is localized on the boundary sites only. We explicitly demonstrate and compute such a bound in two important models in one dimension: in the (isotropic) Heisenberg spin 1/2 chain and in the fermionic Hubbard chain.
