Quantum many-body scars and Kramers-Wannier duality

Weslei B. Fontana¹, Fabrizio Oliviero^2,1*, Yi-Ping Huang^1,2,3

¹Department of physics, National Tsing Hua University, Hsinchu 30013, Taiwan
²Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
³Institute of Physics, Academia Sinica, Taipei 115, Taiwan

* Presenter:Fabrizio Oliviero, email:fabrizio@phys.ncts.ntu.edu.tw

In this work, we consider a particular class of Hamiltonians known as stochastic matrix form (SMF) Hamiltonians, for which there exists a systematic framework to construct exact quantum many-body scar (QMBS) states at zero energy. We focus on a one-dimensional SMF Hamiltonian that hosts QMBS subspaces connected by a Kramers–Wannier duality, implemented via a sequential quantum circuit (SQC). Using sequential quantum circuits, we show that this duality controls the stability of quantum many-body scars in a nonintegrable model, with stability determined by whether the dual preserves scarring conditions. Agreement between perturbation theory and numerics highlights that scar dynamics persist despite chaotic spectra, suggesting that non-invertible dualities can both generate new QMBS and serve as diagnostics for their stability.

Keywords: quantum many-body scar , Kramers–Wannier duality, sequential quantum circuit , stochastic matrix form