# Driven/Floquet Localization & Symmetry Engineering
⏎
**Anchor paper:** K. Agarwal, I. Martin, "Dynamical enhancement of symmetries in many-body systems," *Phys. Rev. Lett.* 125, 080602 (2020). [preprint titled "Polyfractal driving for engineering Hamiltonians and symmetries," arXiv:1905.06389]
⏎
## Background
Static many-body Hamiltonians are stuck with whatever symmetries their microscopic couplings happen to respect. Periodic (Floquet) driving was known to modify effective dynamics — echo sequences suppress unwanted couplings, and disorder-assisted driving can delay heating — with isolated examples showing driving could even generate a new emergent symmetry. What was missing was a systematic recipe: given an arbitrary Hamiltonian, how do you design a drive to enhance a *chosen* symmetry (or several, possibly non-commuting) while keeping the effective Hamiltonian local and avoiding runaway heating?
⏎
## New results
The authors construct a "polyfractal" dynamical-decoupling protocol: symmetry operators applied recursively at nested, self-similar time intervals rather than a single periodic pulse train. This hierarchical construction can simultaneously imprint multiple symmetries onto the effective Floquet Hamiltonian, with symmetry-violating terms suppressed layer-by-layer while the heating timescale stays stretched-exponentially long — an optimal number of layers balances symmetry accuracy against heating. When the engineered symmetries anticommute, this produces a robust degeneracy structure across the whole many-body spectrum, relevant to topologically protected qubits.
⏎
![Polyfractal driving protocol schematic](https://arxiv.org/html/1905.06389v2/polyfract_protocol.png)
*Schematic of the polyfractal driving protocol: symmetry-generating unitaries applied recursively at self-similar nested time intervals, building the Floquet unitary hierarchically layer by layer.*
⏎
## Related work in this direction
- K. Agarwal, S. Ganeshan, R.N. Bhatt, "Localization and transport in a strongly driven Anderson insulator," PRB 96, 014201 (2017).
- S. Ganeshan, K. Agarwal, R.N. Bhatt, "Floquet dynamics of disordered bands with isolated critical energies," PRB (2020).
⏎
Both study how strong periodic driving reshapes localization and transport in disordered systems — the natural extension of the Griffiths/MBL physics one level up, once driving is added.
⏎
**Many-Body Scars from Floquet Automata** is nested here: a specific, further-engineered case of using driving (via automaton circuit structure) to construct a *particular* kind of ergodicity-breaking dynamics.
⏎
⏎
# Parents
⏎
* Many-Body Localization & Griffiths Effects⏎