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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Correlations\, area laws\, and stability of open a
nd thermal many-body quantum systems\n - Eisert\,
J (Freie Universitt Berlin)
DTSTART;TZID=Europe/London:20131031T140000
DTEND;TZID=Europe/London:20131031T150000
UID:TALK48620AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/48620
DESCRIPTION:Investigating scaling laws of correlations and ent
anglement\, stability and simulatability of quantu
m states on spin lattice systems is a central topi
c in Hamiltonian complexity theory. In this talk\,
we discuss open systems and thermal analogues of
features of ground states of quantum many-body sys
tems\, using proof tools inspired by ideas of quan
tum information theory. For open systems\, we esta
blish a connection between mixing times - either c
aptured by Liouvillian gaps or Log-Sobolev-constan
ts independent of the system size - and the cluste
ring of correlations and area laws. For Gibbs stat
es\, we prove that above a universal critical temp
erature only depending on local properties of the
Hamiltonian's interaction hypergraph\, thermal qua
ntum states of local Hamiltonians are stable again
st distant Hamiltonian perturbations. As a consequ
ence\, local expectation values can be approximate
d in polynomial time. The stability theorem also p
rovides a definition of temperature as a local qua
ntity. We prove our clustering result via a reduct
ion to a cluster expansion originally used to appr
oximate thermal states by matrix product operators
.\n\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:Mustapha Amrani
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