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

• URL: http://arxiv.org/abs/2601.20058v1
• Date: Tue, 27 Jan 2026 21:08:54 GMT
• Title: Superfluidity in the spin-1/2 XY model with power-law interactions
• Abstract summary: In trapped-ion quantum simulators, effective spin-1/2 XY interactions can be engineered via laser-induced coupling.<n>We show how conventional superfluidity in the $1d$ XY model is enhanced in the long-range interacting regime.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $α\rightarrow 0$ 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 $α_c$.

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