Tensor networks demonstrate the robustness of localization and symmetry protected topological phases

Abstract

We prove that all eigenstates of many-body localized symmetry protected topological systems with time reversal symmetry have four-fold degenerate entanglement spectra in the thermodynamic limit. To that end, we employ unitary quantum circuits where the number of sites the gates act on grows linearly with the system size. We find that the corresponding matrix product operator representation has similar local symmetries as matrix product ground states of symmetry protected topological phases. Those local symmetries give rise to a ${\mathbb{Z}}_2$ topological index, which is robust against arbitrary perturbations so long as they do not break time reversal symmetry or drive the system out of the fully many-body localized phase.

24 pages (4 pages non-technical summary), v2: minor changes, v3: accepted version

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Cited by in corpus (11)

• Tensor networks for complex quantum systems
• Signatures of the Many-body Localized Regime in Two Dimensions
• Local integrals of motion detection of localization-protected topological order
• Local Integrals of Motion for Topologically Ordered Many-Body Localized Systems
• Classification of symmetry-protected topological phases in two-dimensional many body-localized systems
• Classification of symmetry-protected topological many-body localized phases in one dimension
• Many-body-localization induced protection of symmetry-protected topological order in a XXZ spin model
• Exact projected entangled pair ground states with topological Euler invariant
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• Quantum Circuits Reproduce Experimental Two-dimensional Many-body Localization Transition Point
• Two-dimensional many-body localized systems coupled to a heat bath