  Quasi-one-dimensional lattice systems such as flux ladders with artificial
gauge fields host rich quantum-phase diagrams that have attracted great
interest. However, so far, most of the work on these systems has concentrated
on zero-temperature phases while the corresponding finite-temperature regime
remains largely unexplored. The question if and up to which temperature
characteristic features of the zero-temperature phases persist is relevant in
experimental realizations. We investigate a two-leg ladder lattice in a uniform
magnetic field and concentrate our study on chiral edge currents and
momentum-distribution functions, which are key observables in ultracold
quantum-gas experiments. These quantities are computed for hard-core bosons as
well as noninteracting bosons and spinless fermions at zero and finite
temperatures. We employ a matrix-product-state based purification approach for
the simulation of strongly interacting bosons at finite temperatures and
analyze finite-size effects. Our main results concern the
vortex-fluid-to-Meissner crossover of strongly interacting bosons. We
demonstrate that signatures of the vortex-fluid phase can still be detected at
elevated temperatures from characteristic finite-momentum maxima in the
momentum-distribution functions, while the vortex-fluid phase leaves weaker
fingerprints in the local rung currents and the chiral edge current. In order
to determine the range of temperatures over which these signatures can be
observed, we introduce a suitable measure for the contrast of these maxima. The
results are condensed into a finite-temperature crossover diagram for hard-core
bosons.
