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This work is concerned with thermal quantum states of Hamiltonians on spin and fermionic lattice systems with short range interactions. We provide results leading to a local definition of temperature, thereby extending the notion of "intensivity of temperature'' to interacting quantum models. More precisely, we derive a perturbation formula for thermal states. The influence of the perturbation is exactly given in terms of a generalized covariance. For this covariance we prove exponential clustering of correlations above a universal critical temperature, which upper bounds physical critical temperatures such as the Curie temperature. As a corollary, we obtain that above a the critical temperature, thermal states are stable against distant Hamiltonian perturbations. Moreover, our results imply that above the critical temperature local expectation values can be approximated with a computational cost independent of the system size.

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Dr. Martin Kliesch, FU Berlin
Seminar room 0.03, ETP
Contact: David Gross