Mathematics of operator growth in quantum many-body systems

Event Dates: 

Friday, December 6, 2019 - 12:00pm

CTQM Seminar Type: 

  • CTQM Discussion

Seminar Location: 

  • Duane Physics Room G126

Speaker Name(s): 

Andy Lucas

Speaker Affiliation(s): 

University of Colorado Boulder

Abstract, Event Details: 

The Lieb-Robinson theorem is a classic result in mathematical physics which proves that in a quantum system with local interactions, the commutators of local operators essentially vanish outside of a “light cone” with an emergent, finite velocity.  This result has numerous applications, from bounding classical simulatability of quantum systems to constraining entanglement growth, and many-body operator growth and chaos.   In this talk, I will present new frameworks for understanding operator growth and chaos in quantum many-body systems, both with local and without local interactions, which provide qualitative improvements over existing techniques.  Using these techniques, I will prove two previously open problems in the community: (1) in spin chains with interactions that fall off with distance faster than 1/r^3, commutators of local operators can be made arbitrarily small outside of a “linear light cone” which grows at a finite velocity, just as in local systems; (2) the scrambling time for an operator to grow large in the Sachdev-Ye-Kitaev model of N fermions grows no slower than log N, when N is large but finite.

Research Category: