III. Atomic Stability and Conservation Laws

L. Pičman

Asmi Haldar, Das, Anirban, Chaudhuri, Sagnik +5 more

The ergodicity postulate, a foundational pillar of Gibbsian statistical mechanics predicts that a periodically driven (Floquet) system in the absence of any conservation law heats to a featureless `infinite temperature' state. Here, we find--for a clean and interacting generic spin chain subject to a {\it strong} driving field--that this can be prevented by the emergence of {\it approximate but stable} conservation-laws not present in the undriven system. We identify their origin: they do not necessarily owe their stability to familiar protections by symmetry, topology, disorder, or even high energy costs. We show numerically, {\it in the thermodynamic limit,} that when required by these emergent conservation-laws, the entanglement-entropy density of an infinite subsystem remains zero over our entire simulation time of several decades in natural units. We further provide a recipe for designing such conservation laws with high accuracy. Finally, we present an ensemble description, which we call the strongly driven ensemble incorporating these constraints. This provides a way to control many-body chaos through stable Floquet-engineering. Strong signatures of these conservation-laws should be experimentally accessible since they manifest in all length and time scales. Variants of the spin model we have used, have already been realized using Rydberg-dressed atoms.

M. G. Raizen

Haobo Ma, Wenlin Zhang

Establish energy and spectral conservation laws under finite-window measurement. Core result: for windowed readout with window w and spectral density \rho, windowed energy E_w=\int Ew(E)\rho(E)dE satisfies: (i) Conservation: under unitary evolution \partial_tE_w=0 when w time-independent; (ii) Covariance: gauge-invariant under phase transformations; (iii) NPE closure: discrete approximation with alias+EM+tail error decomposition.