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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Correlations, area laws, and stability of open and thermal many-body quantum systems

## Correlations, area laws, and stability of open and thermal many-body quantum systemsAdd to your list(s) Download to your calendar using vCal - Eisert, J (Freie Universitt Berlin)
- Thursday 31 October 2013, 14:00-15:00
- Seminar Room 2, Newton Institute Gatehouse.
If you have a question about this talk, please contact Mustapha Amrani. Mathematical Challenges in Quantum Information Investigating scaling laws of correlations and entanglement, stability and simulatability of quantum states on spin lattice systems is a central topic in Hamiltonian complexity theory. In this talk, we discuss open systems and thermal analogues of features of ground states of quantum many-body systems, using proof tools inspired by ideas of quantum information theory. For open systems, we establish a connection between mixing times – either captured by Liouvillian gaps or Log-Sobolev-constants independent of the system size – and the clustering of correlations and area laws. For Gibbs states, we prove that above a universal critical temperature only depending on local properties of the Hamiltonian’s interaction hypergraph, thermal quantum states of local Hamiltonians are stable against distant Hamiltonian perturbations. As a consequence, local expectation values can be approximated in polynomial time. The stability theorem also provides a definition of temperature as a local quantity. We prove our clustering result via a reduction to a cluster expansion originally used to approximate thermal states by matrix product operators. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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