Glassy word problems: ultraslow relaxation, Hilbert space jamming, and computational complexity

Understand

We introduce a family of local models of dynamics based on ``word problems'' from computer science and group theory, for which we can place rigorous lower bounds on relaxation timescales.

• These models can be regarded either as random circuit or local Hamiltonian dynamics, and include many familiar examples of constrained dynamics as special cases.
• The configuration space of these models splits into dynamically disconnected sectors, and for initial states to relax, they must ``work out'' the other states in the sector to which they belong.
• When this problem has a high time complexity, relaxation is slow.