We show that the subregion entanglement Hamiltonians of excited eigenstates a quantum many-body system are approximately linear combinations subregionally (quasi)local approximate conserved quantities, with relative commutation errors $\mathcal{O}\left(\frac{\text{subregion boundary area}}{\text{subregion volume}}\right)$. By diagonalizing an Hamiltonian superdensity matrix (EHSM) for ensemble ...

We introduce the notion of cumulants as applied to linear maps between associative (or commutative) algebras that are not compatible with algebraic product structure. These have a close relationship $$A_{\infty }$$ and $$C_{\infty morphisms, which classical homotopical tools for analyzing deformations algebraically maps. look at these two different perspectives understand how infinity-morphisms...

We provide a unified semiclassical theory for the conserved current of nonconserved quantities, and manifest it in two physical contexts: spin Bloch electrons charge mean-field Bogoliubov quasiparticles. Several longstanding problems that limit playground are solved. reveal hitherto overlooked torque quadrupole density Berry phase correction to dipole essential assure circulating with vanishing...