Fig. 4: Theoretical analysis of the relevant many-body states for ωh = 0, Δ↑ = Δ↓ ≡ Δ and a Néel-ordered initial state.
From: Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
a Density of states in the full Hilbert space \({{{\mathcal{H}}}}\) restricted to quarter filling and zero magnetization for the numerical fragments \({{{{\mathcal{N}}}}}_{1}\) (ϵ = 1%), \({{{{\mathcal{N}}}}}_{10}\) (ϵ = 10%), U = 5J, Δ = 3J and \({T}_{{{{\mathcal{N}}}}}=1000\tau\), normalized to the maximum in \({{{\mathcal{H}}}}\); L = 15. b Scaling of the finite-time connectivity \({{{{\mathcal{C}}}}}_{\epsilon }\) with system size for a time window \({T}_{{{{\mathcal{N}}}}}=1000\tau\), U = 5J and Δ = 3J. Solid lines are exponential fits to the data. Dashed lines are the prediction for the finite-time connectivity of a thermal state, showing a constant scaling at 1 − ϵ. c Normalized intersection for U = Ures between the Krylov subspace \({{{{\mathcal{K}}}}}^{{{{\rm{res}}}}}\) and the numerical fragment \({{{{\mathcal{N}}}}}_{\epsilon ({{{{\mathcal{K}}}}}^{{{{\rm{res}}}}})}\) (Methods), where \(\,{{\mbox{dim}}}\,({{{{\mathcal{N}}}}}_{\epsilon ({{{{\mathcal{K}}}}}^{{{{\rm{res}}}}})})=\,{{\mbox{dim}}}\,({{{{\mathcal{K}}}}}^{{{{\rm{res}}}}})\) (main text). The schematic shows the most important processes, connecting the states within the Krylov subspace \({{{{\mathcal{K}}}}}^{{{{\rm{res}}}}}\) (Supplementary Note 4). Inset: Normalized intersection as in the main plot for Δ = 3J. The dashed line illustrates the resonance condition in regime ①.
