Non-Abelian eigenstate thermalization hypothesis

Understand

The eigenstate thermalization hypothesis (ETH) explains why chaotic quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries.

• If the Hamiltonian conserves one quantity ("charge"), the ETH implies thermalization within a charge sector -- in a microcanonical subspace.
• But quantum systems can have charges that fail to commute with each other and so share no eigenbasis; microcanonical subspaces may not exist.
• Furthermore, the Hamiltonian will have degeneracies, so the ETH need not imply thermalization.