Weak-ergodicity-breaking via lattice supersymmetry
Federica Maria Surace, Giuliano Giudici, Marcello Dalmonte
Abstract
We study the spectral properties of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>D</mml:mi></mml:math>-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math> supersymmetric lattice models. We find systematic departures from the eigenstate thermalization hypothesis (ETH) in the form of a degenerate set of ETH-violating supersymmetric (SUSY) doublets, also referred to as many-body scars, that we construct analytically. These states are stable against arbitrary SUSY-preserving perturbations, including inhomogeneous couplings. For the specific case of two-leg ladders, we provide extensive numerical evidence that shows how those states are the only ones violating the ETH, and discuss their robustness to SUSY-violating perturbations. Our work suggests a generic mechanism to stabilize quantum many-body scars in lattice models in arbitrary dimensions.