期刊
PHYSICAL REVIEW LETTERS
卷 112, 期 21, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.112.210601
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资金
- Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP)
- National Research Foundation of South Africa via the Incentive Funding
- Competitive Programme for Rated Researchers
Lieb-Robinson-type bounds are reported for a large class of classical Hamiltonian lattice models. By a suitable rescaling of energy or time, such bounds can be constructed for interactions of arbitrarily long range. The bound quantifies the dependence of the system's dynamics on a perturbation of the initial state. The effect of the perturbation is found to be effectively restricted to the interior of a causal region of logarithmic shape, with only small, algebraically decaying effects in the exterior. A refined bound, sharper than conventional Lieb-Robinson bounds, is required to correctly capture the shape of the causal region, as confirmed by numerical results for classical long-range XY chains. We discuss the relevance of our findings for the relaxation to equilibrium of long-range interacting lattice models.
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