Data from: Emergent electrostatics in planar XY spin models: The bridge connecting topological order with broken U(1) symmetry

Topological phases have been a central focus of condensed-matter physics
for over 50 years.  Along with many experimental applications,
they have provided much intellectual interest due to their
characterization via some form of topological ordering, as opposed to the
symmetry-breaking ordering of conventional continuous phase transitions.
 This distinction is most subtle in the case of the
Berezinskii—Kosterlitz—Thouless (BKT) transition as its experimental
realizations appear to break U(1) symmetry at low temperature.
 It also presents two further paradoxes: i) its prototypical
short-range interacting planar XY spin model behaves as an emergent
long-range interacting electrolyte; ii) its topological ordering is not
accompanied by a topological nonergodicity within the BKT picture.
 This data deposit supports a review paper that addresses these
three interconnected questions.  In particular, it provides the
simulation data that supports the concept of topological nonergodicity
throughout the low-temperature phase.  Simulation data that
supports the concept of broken U(1) symmetry (at low temperature) is
reproduced from another research article.  This data was stored
in the University of Bristol data repository, data.bris, with DOI
10.5523/bris.3ov1rl6xtshwv2iuixrbs6f39q.  Simulation data used to
demonstrate low-temperature broken symmetry in the two-dimensional Ising
model is also provided in the present data deposit.