Single-quasiparticle eigenstate thermalization

Quadratic Hamiltonians that exhibit single -particle quantum chaos are called quantum -chaotic quadratic Hamiltonians. One of their hallmarks is single -particle eigenstate thermalization introduced in Lydzba et al. [Phys. Rev. B 104, 214203 (2021)], which describes statistical properties of matrix elements of observables in single -particle eigenstates. However, the latter has been studied only in quantum -chaotic quadratic Hamiltonians that obey the U(1) symmetry. Here, we focus on quantum -chaotic quadratic Hamiltonians that break the U(1) symmetry and, hence, their "single -particle" eigenstates are actually single-quasiparticle excitations introduced on the top of a many -body state. We study their wave functions and matrix elements of one -body observables, for which we introduce the notion of single-quasiparticle eigenstate thermalization. Focusing on spinless fermion Hamiltonians in three dimensions with local hopping, pairing, and on -site disorder, we also study the properties of disorder -induced near zero modes, which give rise to a sharp peak in the density of states at zero energy. Finally, we numerically show equilibration of observables in many -body eigenstates after a quantum quench. We argue that the latter is a consequence of single-quasiparticle eigenstate thermalization, in analogy to the U(1) symmetric case from Lydzba et al. [Phys. Rev. Lett. 131, 060401 (2023)].