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 systems

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Mustapha Amrani.

This talk has been canceled/deleted

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.

Tell a friend about this talk:

This talk is included in these lists:

This talk is not included in any other list

Note that ex-directory lists are not shown.

 

© 2006-2024 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity