Bounded light cone and robust topological order out of equilibrium

• URL: http://arxiv.org/abs/2208.13839v4
• Date: Mon, 28 Oct 2024 14:22:56 GMT
• Title: Bounded light cone and robust topological order out of equilibrium
• Authors: Yu Zeng, Alioscia Hamma, Yu-Ran Zhang, Jun-Peng Cao, Heng Fan, Wu-Ming Liu,
• Abstract summary: Ground state degeneracy of topologically ordered gapped Hamiltonians is the bedrock for self-correcting quantum memories. We show that the emergence of a bounded light cone renders the unitary time evolution a quasi-adiabatic continuation that preserves topological order.
• Score: 6.549122700373228
• License:
• Abstract: The ground state degeneracy of topologically ordered gapped Hamiltonians is the bedrock for self-correcting quantum memories, which are unfortunately not stable away from equilibrium even at zero temperature. This plague precludes practical robust self-correction since stability at zero temperature is a prerequisite for finite-temperature robustness. In this work, we show that the emergence of a bounded light cone renders the unitary time evolution a quasi-adiabatic continuation that preserves topological order, with the initial ground space retaining its macroscopic distance at all times as a quantum code. We also show how bounded light cones can emerge through suitable perturbations in Kitaev's toric code and honeycomb model. Our results suggest that topological orders and self-correcting quantum memories can be dynamically robust at zero temperature.

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