Local integrals of motion detection of localization-protected topological order

Abstract

Many-body-localized (MBL) phases can be topologically distinct, but distinguishing these phases using order parameters can be challenging. Here we show how topologically distinct local integrals of motion, variationally parametrized by quantum circuits, can be used to numerically demonstrate the topological inequivalence of MBL phases. We illustrate our approach on a fermionic chain where both topologically distinct MBL phases and benchmark comparisons to order parameters are possible. We also use our approach, augmented by the DMRG-X algorithm, to extract high-energy topological doublets. We describe applying our methods to higher dimensions to identify MBL topological order and topological multiplets hidden by the dense many-body spectrum.

8 pages, 7 figures; v2: accepted manuscript; v3: typo fixes

References in corpus (12)

• Non-Abelian Anyons and Topological Quantum Computation
• Many body localization and thermalization in quantum statistical mechanics
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Many-body localization edge in the random-field Heisenberg chain
• Many body localization in Heisenberg XXZ magnet in a random field
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Recent progress in many-body localization
• Constructing local integrals of motion in the many-body localized phase
• Many-body localisation implies that eigenvectors are matrix-product states
• Emergent ergodicity at the transition between many-body localized phases
• Robustness of Majorana edge modes and topological order -- exact results for the symmetric interacting Kitaev chain with disorder
• Edge mode locality in perturbed symmetry protected topological order

Cited by in corpus (6)

• Topological order in random interacting Ising-Majorana chains stabilized by many-body localization
• Topological and quantum critical properties of the interacting Majorana chain model
• Quantum information spreading in random spin chains with topological order
• Many-body-localization protection of eigenstate topological order in two dimensions
• Renormalization view on resonance proliferation between many-body localized phases
• Quantum Circuits Reproduce Experimental Two-dimensional Many-body Localization Transition Point