Physics Theory Seminar with Andrew Lucas on Speed limits and locality in many-body quantum dynamics
Information cannot travel faster than the speed of light. Still, in many practical settings (such as listening to sound), emergent speed limits on information can be far slower than the limit set by relativity. In 1972, Lieb and Robinson proved that quantum correlations and information propagate with a finite velocity in (non-relativistic) quantum many-body spin systems with nearest neighbor interactions. In practical systems, these speed limits are orders of magnitude smaller than the speed of light. Five decades later, the Lieb-Robinson Theorem has become one of the most important results in mathematical quantum physics. I will introduce and motivate the Lieb-Robinson Theorem, and overview our recent generalizations of the Lieb-Robinson Theorem to systems with power-law interactions, bosonic models, and dynamics with measurement. These bounds place tight constraints on how fast information can be shuttled through any future quantum computer. I will also highlight a number of surprising applications of Lieb-Robinson bounds to many-body physics: the computational cost of simulating many-body dynamics on classical and quantum computers, revealing the properties of gapped phases, and proving the existence and metastability of the false vacuum. These results highlight how locality can play a central role inconstraining what is possible in quantum systems.
This lecture was made possible by the William C. Ferguson fund.