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Condensed Matter Seminar - Andy Lucas (University of Colorado) - "Mathematics of Operator Growth in Quantum Many-body Systems"

Andy Lucas (University of Colorado) 2/4/20 colloquium speaker
February 3, 2020
11:30AM - 12:30PM
1080 Physics Research Building, Smith Seminar room @ 11:30am

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Add to Calendar 2020-02-03 11:30:00 2020-02-03 12:30:00 Condensed Matter Seminar - Andy Lucas (University of Colorado) - "Mathematics of Operator Growth in Quantum Many-body Systems" 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. 1080 Physics Research Building, Smith Seminar room @ 11:30am Department of Physics physics@osu.edu America/New_York public

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.