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 $α_c$ .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 $α_c$.

cond-mat.quant-gasCross-listedarXiv:2601.20058Physical review. B./Physical review. BJan 29, 20260 citations

Entanglement in (1/2,1) mixed-spin XY model with long-range interactions

Seyit Deniz Han, Tuĝba Tüfekçi, Timothy P. Spiller +1 more

In this study, considering the long-range interaction with an inverse-square and its trigonometric and hyperbolic variants in SCM model we investigate entanglement in (1/2,1) mixed-spin XY model. We also discuss the temperature and magnetic field dependence of the thermal entanglement in this system for different types of interaction. The numerical results show that, in the presence of the long-range interactions, thermal entanglement between spins has a rich behavior dependent upon the interaction strength, temperature and magnetic field. Indeed we find that for less than a critical distance there are entanglement plateaus dependent upon the distance between the spins, whereas above the critical distance the entanglement can exhibit sudden death.In this study, considering the long-range interaction with an inverse-square and its trigonometric and hyperbolic variants in SCM model we investigate entanglement in (1/2,1) mixed-spin XY model. We also discuss the temperature and magnetic field dependence of the thermal entanglement in this system for different types of interaction. The numerical results show that, in the presence of the long-range interactions, thermal entanglement between spins has a rich behavior dependent upon the interaction strength, temperature and magnetic field. Indeed we find that for less than a critical distance there are entanglement plateaus dependent upon the distance between the spins, whereas above the critical distance the entanglement can exhibit sudden death.

arXiv:1111.2694Nov 11, 20110 citations

Quantum Correlations in Infinite XY Spin-1/2 Chains and Quantum Phase Transition

Xiaodong Tan, Shou-Sheng Huang, Bai-Qi Jin

We examine the ability of quantum discord (QD) and entanglements (concurrence, EoF and negativity) to detect the critical points associated to quantum phase transitions (QPTs) for XY models, i.e., the isotropic XY model with three-spin interactions at zero temperature, and the anisotropic XY model in a transverse magnetic field h at finite temperatures. For the case of zero temperature, we found that both entanglements and QD can spotlight the critical points of QPTs for these two models. Moreover, QD versus distance M exhibits the long-range behavior of quantum correlation for the anisotropic XY model, while entanglement is short-ranged. For the case of finite temperatures, we found that negativity has the same behaviors with concurrence at or near transition points. Moreover, QD for the anisotropic XY model can increase with temperature even in the absence of a magnetic field.We examine the ability of quantum discord (QD) and entanglements (concurrence, EoF and negativity) to detect the critical points associated to quantum phase transitions (QPTs) for XY models, i.e., the isotropic XY model with three-spin interactions at zero temperature, and the anisotropic XY model in a transverse magnetic field h at finite temperatures. For the case of zero temperature, we found that both entanglements and QD can spotlight the critical points of QPTs for these two models. Moreover, QD versus distance M exhibits the long-range behavior of quantum correlation for the anisotropic XY model, while entanglement is short-ranged. For the case of finite temperatures, we found that negativity has the same behaviors with concurrence at or near transition points. Moreover, QD for the anisotropic XY model can increase with temperature even in the absence of a magnetic field.

Communications in Theoretical PhysicsFeb 1, 20139 citations

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