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Q: Fachverband Quantenoptik und Photonik

Q 58: Quantum information: Concepts and methods IV

Q 58.6: Vortrag

Freitag, 21. März 2014, 11:45–12:00, Kinosaal

Locality of temperature — •Martin Kliesch, Christian Gogolin, Michael J. Kastoryano, Arnau Riera, and Jens Eisert — Freie Universität Berlin

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, which has been an open problem in the context of nanoscale systems. Technically, we derive a truncation formula for thermal states. The truncation error is exactly given by a generalized covariance. For this covariance we prove exponential clustering of correlations above a universal critical temperature. The proof builds on a percolation argument originally used to approximate thermal states by matrix-product operators. As a corollary we obtain that above a the critical temperature, thermal states are stable against distant Hamiltonian perturbations and we obtain a model independent upper bound on critical temperatures, such as the Curie temperature. Moreover, our results imply that above the critical temperature local expectation values can be approximated efficiently in the error and the system size.