Title | Non-Abelian eigenstate thermalization hypothesis |

Publication Type | Journal Article |

Year of Publication | 2022 |

Authors | Murthy, C, Babakhani, A, Iniguez, F, Srednicki, M, Halpern, NYunger |

Date Published | 6/10/2022 |

Keywords | FOS: Physical sciences, High Energy Physics - Theory (hep-th), Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph), Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el) |

Abstract | 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. 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 observables' time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we also 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. |

URL | https://arxiv.org/abs/2206.05310 |

DOI | 10.48550/ARXIV.2206.05310 |