Local Integrals of Motion for Topologically Ordered Many-Body Localized
Systems
- URL: http://arxiv.org/abs/2001.03167v3
- Date: Fri, 24 Jul 2020 06:23:29 GMT
- Title: Local Integrals of Motion for Topologically Ordered Many-Body Localized
Systems
- Authors: Thorsten B. Wahl, Benjamin B\'eri
- Abstract summary: Many-body localized (MBL) systems are often described using their local integrals of motion.
We show that this assumption cannot hold for topologically ordered MBL systems.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Many-body localized (MBL) systems are often described using their local
integrals of motion, which, for spin systems, are commonly assumed to be a
local unitary transform of the set of on-site spin-z operators. We show that
this assumption cannot hold for topologically ordered MBL systems. Using a
suitable definition to capture such systems in any spatial dimension, we
demonstrate a number of features, including that MBL topological order, if
present: (i) is the same for all eigenstates; (ii) is robust in character
against any perturbation preserving MBL; (iii) implies that on topologically
nontrivial manifolds a complete set of integrals of motion must include
nonlocal ones in the form of local-unitary-dressed noncontractible Wilson
loops. Our approach is well suited for tensor-network methods, and is expected
to allow these to resolve highly-excited finite-size-split topological
eigenspaces despite their overlap in energy. We illustrate our approach on the
disordered Kitaev chain, toric code, and X-cube model.
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