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 ($1\text{D}$) traps, these interactions decay as a power-law with distance $1/r^{\alpha }$, with a tunable exponent $\alpha$. For small $\alpha$, 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 ${\alpha }_c$ from the lens of the spin stiffness, or superfluid density. We develop a stochastic series expansion 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 $\alpha \to 0$ 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 ${\alpha }_c$.

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• Magnetism
• Quantum phase transitions
• Superfluidity
• Trapped ions
• Linear spin wave theory
• Quantum Monte Carlo
• XY model