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X-ORIGINAL-URL:https://www.ift.uam-csic.es
X-WR-CALDESC:Events for Instituto de Física Teórica
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DTSTART;TZID=Europe/Madrid:20251014T113000
DTEND;TZID=Europe/Madrid:20251014T130000
DTSTAMP:20260405T202257
CREATED:20251008T090655Z
LAST-MODIFIED:20251125T081258Z
UID:23262-1760441400-1760446800@www.ift.uam-csic.es
SUMMARY:Holo Club: Explicit Connections Between Krylov and Nielsen Complexity
DESCRIPTION:Speaker: Le-Chen Qu (IFT) \n\nVenue&Time: Grey Room 3 / 11:30 \n\nAbstract: We establish a precise correspondence between Krylov complexity and Nielsen complexity in quantum many-body systems. By identifying the Krylov basis with the generators of elementary gates in Nielsen’s geometric framework\, the Krylov complexity of precursor operators acquires a geometric interpretation as the length of straight-line paths in Nielsen geometry. This construction provides an upper bound on Nielsen complexity\, which becomes exact in the small-precursor limit. Employing the SYK model as a test case\, we demonstrate that the straight-line trajectory satisfies the Nielsen geodesic equation and remains both locally and globally minimizing up to a critical value of $z$\, beyond which conjugate points and geodesic loops arise. Within this framework\, cost functions quadratic in the Krylov index are further shown to reproduce the conjectured proportionality between the complexity growth rate and the operator size.
URL:https://www.ift.uam-csic.es/event/holo-club-explicit-connections-between-krylov-and-nielsen-complexity/
LOCATION:Gray Room 3\, Instituto de Física Teórica (IFT) -C. Nicolás Cabrera\, 13-15\, Fuencarral-El Pardo\, Madrid\, 28049\,\, Spain
CATEGORIES:Journal clubs,Scientific activities
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DTSTART;TZID=Europe/Madrid:20251014T140000
DTEND;TZID=Europe/Madrid:20251014T150000
DTSTAMP:20260405T202257
CREATED:20251008T110737Z
LAST-MODIFIED:20251125T081258Z
UID:23278-1760450400-1760454000@www.ift.uam-csic.es
SUMMARY:Cosmology Journal Club
DESCRIPTION:Every Tuesday at 2:00 PM in the discussion room on the 5th floor. \nJoin the IFT cosmology/gravity journal club at benty-fields.com to vote for papers and volunteer to present them.
URL:https://www.ift.uam-csic.es/event/cosmology-journal-club-2/
LOCATION:Discussion room 5th floor\, C. Nicolás Cabrera\, 13-15\, Fuencarral-El Pardo\, Madrid\, Madrid\, 28049\, Spain
CATEGORIES:Journal clubs,Scientific activities
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