Lieb-Robinson bounds with dependence on interaction strengths

Details Lieb-Robinson bounds with dependence on interaction strengths Lieb-Robinson bounds with dependence on interaction strengths

2010-02-22

arxiv.org/abs/1002.4190v2

Physical Review A (Vol.81, No.6) (2010)

Physics

Mathematical Physics

19 pages, 1 figure, minor modifications

Scientific paper

10.1103/PhysRevA.81.062107

We propose new Lieb-Robinson bounds (bounds on the speed of propagation of information in quantum systems) with an explicit dependence on the interaction strengths of the Hamiltonian. For systems with more than two interactions it is found that the Lieb-Robinson speed is not always algebraic in the interaction strengths. We consider Hamiltonians with any finite number of bounded operators and also a certain class of unbounded operators. We obtain bounds and propagation speeds for quantum systems on lattices and also general graphs possessing a kind of homogeneity and isotropy. One area for which this formalism could be useful is the study of quantum phase transitions which occur when interactions strengths are varied.

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