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DTSTAMP:20260921T150126Z
LAST-MODIFIED:20180208T195424Z
DTSTART:20180212T160000Z
DTEND:20180212T170000Z
UID:event1887@bu.edu
URL:http://physics.bu.edu/internal/events/show/1887
SUMMARY:"Operator Spreading and the Quantum Butterfly Effect in Random Unit
	ary Circuits"
DESCRIPTION:Featuring Sagar Vijay\, Massachusetts Institute of Technology\n
	Hosted by: Philip Crowley\n\nPart of the Condensed Matter Theory Seminar Se
	ries.\n\nWe provide universal\, long-distance descriptions for the ‘quant
	um butterfly effect’\, which describes the spreading of a local disturban
	ce in a quantum medium\, and is quantified by the ‘out-of-time-order corr
	elator’ (OTOC).  We obtain these results by studying quantum circuits mad
	e of random unitaries\, which yield minimally structured models for chaotic
	 quantum dynamics\, and are able to capture universal properties of quantum
	 entanglement growth.  In this setting\, we demonstrate a mapping between t
	he OTOC and classical growth processes\, which leads to exact results and e
	xplicit universal scaling forms for the OTOC. \nIn 1+1D\, we demonstrate th
	at the OTOC satisfies a biased diffusion equation\, which gives exact resul
	ts for its spatial profile\, and for the butterfly speed. In higher dimensi
	ons\, we show that the averaged OTOC can be understood exactly via a corres
	pondence with a classical droplet growth problem. We support our analytic a
	rgument with simulations in 2+1D and demonstrate that in a lattice model\, 
	the late time shape of the spreading operator is in general not spherical. 
	However when full spatial rotational symmetry is present in 2+1D\, our mapp
	ing implies an exact asymptotic form for the OTOC in terms of the Tracy-Wid
	om distribution. For an alternative perspective on the OTOC in 1+1D\, we ma
	p it to the partition function of an Ising-like model. As a result of speci
	al structure arising from unitarity\, this partition function reduces to a 
	random walk calculation which can be performed exactly.  We argue that the 
	coarse-grained pictures carry over to operator spreading in generic many-bo
	dy systems.
LOCATION:SCI 328\, 590 Commonwealth Avenue\, 02215
STATUS:CONFIRMED
CLASS:PUBLIC
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