Localization-Protected Quantum Order

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Systems that are many-body Anderson localized can exhibit symmetry-breaking long-range order or topological order in regimes where such order would be destroyed at equilibrium by thermal fluctuations. The ordering is dynamical: an ordered initial state stays ordered, being "protected" by the localization of all fluctuations. The simplest examples are quantum Ising models with static randomness. For the random quantum Ising chain this feature has been "known" but apparently not appreciated for close to half a century.

Ref.: Huse, et al., Phys. Rev. B 88, 014206 (2013).