Is quasiperiodic localization stable in two dimensions? · revision history

Revision 2

Accepted · core change · record

Changes against revision 1:

Title · changed
Revision 1: Is quasiperiodic localization stable in two dimensions
Revision 2: Is quasiperiodic localization stable in two dimensions?
Plain
A non-random but irregular potential, built from waves whose wavelengths have an irrational ratio to the lattice spacing (quasiperiodic), has no rare weak spots, so the rare-region argument may not apply. Whether such systems localize in two dimensions is open.
Precise · changed · core
Revision 1: Interacting bosons or fermions on a square lattice in the quasiperiodic potential $V_i = V [\operatorname{cos}(2 \pi \beta x_i + \phi_x) + \operatorname{cos}(2 \pi \beta y_i + \phi_y)]$ with irrational $\beta$: is there $V_c$ such that local memory persists at infinite time as $L \to \infty$? Answer yes or no.
Revision 2: Interacting bosons or fermions on a square lattice in the quasiperiodic potential $V_i = V [\cos(2 \pi \beta x_i + \phi_x) + \cos(2 \pi \beta y_i + \phi_y)]$ with irrational $\beta$: is there $V_c$ such that local memory persists at infinite time as $L \to \infty$? Answer yes or no.
Settled by
A size-independent localization crossover over a wide range of L in experiment, together with a theory excluding resonant instabilities in the quasiperiodic case.
Kind
well-posed
Answer type
yes-no
References
(empty)
Literature status
open
Status note · changed
Revision 1: Agrawal, Vasseur, Gopalakrishnan (PRB 106, 094206, 2022) argue it is stable in $d=2$ at strong modulation, and a 2025 optical-lattice experiment up to 24 x 24 sites saw no clear size drift of the quasiperiodic crossover.
Revision 2: Agrawal, Vasseur, Gopalakrishnan (PRB 106, 094206, 2022) argue it is stable in $d=2$ at strong modulation, and a 2025 optical-lattice experiment up to $24 \times 24$ sites saw no clear size drift of the quasiperiodic crossover.
Posed since
(empty)

Decisions