Localization-protected quantum order

TLDR

Closed quantum systems with quenched randomness exhibit many‑body localized regimes that fail to equilibrate even when prepared with macroscopic energy above their ground states. The authors aim to show that such localized systems can order by having individual many‑body eigenstates break symmetries or display topological order in the infinite volume limit. They demonstrate this ordering mechanism by revealing that localized systems can transition between ordered and disordered localized phases via non‑thermodynamic, potentially critical, changes in the properties of their many‑body eigenstates. The findings indicate that isolated localized quantum systems can maintain order at energy densities where thermal systems are disordered, that localization protects against decoherence enabling experimental manipulation of macroscopic quantum states, and that a sharp spectral transition in the Hamiltonian’s statistics accompanies these changes.

Abstract

Closed quantum systems with quenched randomness exhibit many-body localized regimes wherein they do not equilibrate even though prepared with macroscopic amounts of energy above their ground states. We show that such localized systems can order in that individual many-body eigenstates can break symmetries or display topological order in the infinite volume limit. Indeed, isolated localized quantum systems can order even at energy densities where the corresponding thermally equilibrated system is disordered, i.e. : localization protects order. In addition, localized systems can move between ordered and disordered localized phases via non-thermodynamic transitions in the properties of the many-body eigenstates. We give evidence that such transitions may proceed via localized critical points. We note that localization provides protection against decoherence that may allow experimental manipulation of macroscopic quantum states. We also identify a `spectral transition' involving a sharp change in the spectral statistics of the many-body Hamiltonian.