Abstract
We prove that quantum information encoded in some topological excitations, including certain Majorana zero modes, is protected in closed systems for a time scale exponentially long in system parameters. This protection holds even at infinite temperature. At lower temperatures the decay time becomes even longer, with a temperature dependence controlled by an effective gap that is parametrically larger than the actual energy gap of the system. This non-equilibrium dynamical phenomenon is a form of prethermalization, and occurs because of obstructions to the equilibriation of edge or defect degrees of freedom with the bulk. We analyze the ramifications for ordered and topological phases in one, two, and three dimensions, with examples including Majorana and parafermionic zero modes in interacting spin chains. Our results are based on a non-perturbative analysis valid in any dimension, and they are illustrated by numerical simulations in one dimension. We discuss the implications for experiments on quantum-dot chains tuned into a regime supporting end Majorana zero modes, and on trapped ion chains.
Highlights
Solid-state systems supporting non-Abelian anyons, such as Majorana zero modes (MZMs), are the focus of considerable research aimed at exploiting them for quantum information processing [1,2,3,4]
We demonstrate that “prethermalization,” the exponentially slow approach to thermal equilibrium that occurs in some closed quantum systems [26,27,28,29,30,31], can protect edge zero modes and, topological degrees of freedom in higher-dimensional systems as well
We show that prethermalization can extend topological protection into regimes where it might have been expected to fail
Summary
Solid-state systems supporting non-Abelian anyons, such as Majorana zero modes (MZMs), are the focus of considerable research aimed at exploiting them for quantum information processing [1,2,3,4]. We demonstrate that “prethermalization,” the exponentially slow approach to thermal equilibrium that occurs in some closed quantum systems [26,27,28,29,30,31], can protect edge zero modes and, topological degrees of freedom in higher-dimensional systems as well. One particular example we describe in detail is the transverse-field Ising chain perturbed by integrability-breaking interactions While this chain is related to the quantum-dot chain via a Jordan-Wigner transformation, the nonlocality of the map means that topological order in the latter is ordinary ferromagnetic order in the former. IV, we discuss the lifetime of the Majorana zero modes at nonzero temperatures and present numerical simulations supporting our arguments VIII, we consider integrable systems, where the zero modes may survive much longer (possibly even infinitely longer) than the lower bound
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