Complex-Time Singularity and Locality Estimates for Quantum Lattice Systems

Details Complex-Time Singularity and Locality Estimates for Quantum Lattice Systems Complex-Time Singularity and Locality Estimates for Quantum Lattice Systems

2010-11-08

arxiv.org/abs/1011.1875v1

Physics

Mathematical Physics

29 pages, 7 figures

Scientific paper

We present and prove a well-known locality bound for the complex-time dynamics of a general class of one-dimensional quantum spin systems. Then we discuss how one might hope to extend this same procedure to higher dimensions using ideas related to the Eden growth process and lattice trees. Finally, we demonstrate with a specific family of lattice trees in the plane why this approach breaks down in dimensions greater than one and prove that there exist interactions for which the complex-time dynamics blows-up in finite imaginary time.

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