Ergodicity breaking and Localization of the Nicolai supersymmetric fermion lattice model

TL;DR

This paper explores the Nicolai supersymmetric fermion lattice model, revealing its local constants of motion, hidden supersymmetries, and ergodicity breaking, along with discussions on localization properties and quantum integrability.

Contribution

It identifies infinitely many local constants of motion and hidden supersymmetries, demonstrating ergodicity breaking and analyzing localization and integrability in the Nicolai model.

Findings

Existence of infinitely many local fermionic constants of motion.

Presence of hidden local supersymmetries in the model.

Ergodicity breaking in the Nicolai model due to these constants.

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.