Ergodicity breaking and Localization of the Nicolai supersymmetric fermion lattice model

Abstract

We investigate dynamics of the supersymmetric fermion lattice model defined by Hermann Nicolai. We provide its local fermionic constants of motion that exist infinitely many. These generate hidden local supersymmetries that the Nicolai model possesses in addition to its defining dynamical supersymmetry. The existence of such local constants directly implies the breaking ergodicity of the model in the sense of Mazur. At zero temperature, there are infinitely many degenerated classical ground states. We discuss these MBL-like properties. First, we show the delocalization scenario proposed by De Roeck-Huveneers can not naively apply to the Nicolai model at zero temperature despite its disorder-free translation-invariant quantum interaction. Second, we discuss the quantum integrability of the Nicolai model based on the proposal by Caux-Mossel.

25pages, no figure. This is the final version, J Stat Phys (2018)

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• A remark on the notion of independence of quantum integrals of motion in the thermodynamic limit
• Ground states of Nicolai and ${\mathbb{Z}}_2$ Nicolai models
• Topological Quantum Computation on Supersymmetric Spin Chains
• Emergent spacetime supersymmetry in an interacting Kitaev chain with explicit supersymmetry
• Local symmetries and extensive ground-state degeneracy of a 1D supersymmetric fermionic chain