Non-Abelian Eigenstate Thermalization Hypothesis

Abstract

The eigenstate thermalization hypothesis (ETH) explains why nonintegrable 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. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics. Illustrating with SU(2) symmetry, we apply the non-Abelian ETH in calculating local operators' time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we find cases in which, under a physically reasonable assumption, the time average converges to the thermal average unusually slowly as a function of the global-system size. This work extends the ETH, a cornerstone of many-body physics, to noncommuting charges, recently a subject of intense activity in quantum thermodynamics.

Imperfect many-body localization in exchange-disordered isotropic spin chains

“…Related investigations on one dimensional Hubbard chains [39] also support the role of nonabelian symmetries in destabilizing the MBL phase [40][41][42]. Most recently, the effect of nonabelian symmetries on eigenstate thermalization [43] and entanglement entropies [44] has been discussed. In the present work, we report on a study of disordered rotationally invariant spin chains similar to [37,38], but with different disorder distributions and with a focus on spectral properties.…”

Classical route to ergodicity and scarring in collective quantum systems

“…Even in the presence of additional conserved quantities, thermalization in a many-body system can still be achieved for which the steady value of the observables correspond to that of a 'generalized Gibbs ensemble' (GGE) [11][12][13]16]. Recently, the ETH has also been generalized for non-commuting conserved charges [231]. Moreover, ongoing studies have unveiled structure beyond ETH, encompassing the statistical correlations between the matrix elements of the observables as well as the energy eigenstates [232][233][234][235].…”