skip to content
 

Correlations, area laws, and stability of open and thermal many-body quantum systems

Presented by: 
J Eisert Freie Universität Berlin
Date: 
Thursday 31st October 2013 - 14:00 to 15:00
Venue: 
INI Seminar Room 2
Abstract: 
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.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons