Superfluidity in the spin-1/2 XY model with power-law interactions

In trapped-ion quantum simulators, effective spin-1/2 XY interactions can be engineered via laser-induced coupling between internal atomic states and collective phonon modes. In the simplest one-dimensional (1d) traps, these interactions decay as a power-law with distance 1/r^α, with a tunable exponent α. For small α, the resulting long-range 1d XY model exhibits continuous symmetry breaking, in marked contrast to its nearest neighbor counterpart. In this paper, we examine this model near the phase transition at α_c from the lens of the spin stiffness, or superfluid density. We develop a stochastic series expansion (SSE) quantum Monte Carlo (QMC) simulation and a generalized winding number estimator to measure the superfluid density in the presence of power-law interactions, which we test against exact diagonalization for small lattice sizes. Our results show how conventional superfluidity in the 1d XY model is enhanced in the long-range interacting regime. This is observed as a diverging superfluid density as α→ 0 in the thermodynamic limit, which we show is consistent with linear spin-wave theory. Finally, we define a normalized superfluid density estimator that clearly distinguishes the short, medium, and long-range interacting regimes, providing a novel QMC probe of the critical value α_c.