We study the infinite-temperature properties of an infinite sequence of random quantum spin chains using a real-space renormalization group approach, and demonstrate that they exhibit non-ergodic behavior at strong disorder. The analysis is convenien
tly implemented in terms of SU(2)$_k$ anyon chains that include the Ising and Potts chains as notable examples. Highly excited eigenstates of these systems exhibit properties usually associated with quantum critical ground states, leading us to dub them quantum critical glasses. We argue that random-bond Heisenberg chains self-thermalize and that the excited-state entanglement crosses over from volume-law to logarithmic scaling at a length scale that diverges in the Heisenberg limit $krightarrowinfty$. The excited state fixed points are generically distinct from their ground state counterparts, and represent novel non-equilibrium critical phases of matter.
We show that the magnetization of a single `qubit spin weakly coupled to an otherwise isolated disordered spin chain exhibits periodic revivals in the localized regime, and retains an imprint of its initial magnetization at infinite time. We demonstr
ate that the revival rate is strongly suppressed upon adding interactions after a time scale corresponding to the onset of the dephasing that distinguishes many-body localized phases from Anderson insulators. In contrast, the ergodic phase acts as a bath for the qubit, with no revivals visible on the time scales studied. The suppression of quantum revivals of local observables provides a quantitative, experimentally observable alternative to entanglement growth as a measure of the `non-ergodic but dephasing nature of many-body localized systems.
The quantum evolution after a metallic lead is suddenly connected to an electron system contains information about the excitation spectrum of the combined system. We exploit this type of quantum quench to probe the presence of Majorana fermions at th
e ends of a topological superconducting wire. We obtain an algebraically decaying overlap (Loschmidt echo) ${cal L}(t)=| < psi(0) | psi(t) > |^2sim t^{-alpha}$ for large times after the quench, with a universal critical exponent $alpha$=1/4 that is found to be remarkably robust against details of the setup, such as interactions in the normal lead, the existence of additional lead channels or the presence of bound levels between the lead and the superconductor. As in recent quantum dot experiments, this exponent could be measured by optical absorption, offering a new signature of Majorana zero modes that is distinct from interferometry and tunneling spectroscopy.
