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.
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.
**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.
*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.
