Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2601.20058 · Physical review. B./Physical review. B

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

Muhammad Shaeer Moeed, Costanza Pennaforti, Adrian Del Maestro, Roger G. Melko

cond-mat.quant-gascond-mat.stat-mechcond-mat.str-elquant-phSubmitted Jan 27, 2026• Announced Jan 29, 2026• 0 citations• Revised May 8, 2026 (v2)
v1 · Jan 27, 2026v2 · May 8, 2026
arXivHTMLPDF

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 $α_c$.

DOI
10.1103/81fj-tv6w
Comments
17 pages, 10 figures

Related papers

Bose-Hubbard Model with Power-Law Hopping in One Dimension

Tanul Gupta, Nikolay V. Prokof'ev, Guido Pupillo

We investigate the zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as 1/r^{α} using exact large scale quantum Monte Carlo simulations. For all 1<α≤3 the quantum phase transition from a superfluid and a Mott insulator at unit filling is found to be continuous and scale invariant, in marked contrast with the Berezinskii-Kosterlitz-Thouless (BKT) scenario that is recovered only for α>3. By performing finite-size scaling collapses of the superfluid stiffness and extracting dynamical and correlation-length exponents from the low-energy spectrum, we establish that these transitions define a distinct universality class throughout the long-range regime 1<α≤3. Analysis of the single-particle correlation functions and grand canonical phase diagram further reveals a sequence of ordering regimes within the superfluid phase: true long-range order for α≤2, anomalous quasi-long-range order for 2<α≤3, and conventional algebraic decay for α>3. Our exact numerical results provide a benchmark to compare theories of long-range quantum models and are relevant for experiments with cold neutral atom, molecules and ion chains.

arXiv:2412.01571•Physical Review Letters•Apr 15, 2026•2 citations

Quantum spin models with long-range interactions and tunnelings: a quantum Monte Carlo study

Michał Maik, Philipp Hauke, Omjyoti Dutta +2 more

We use a quantum Monte Carlo method to investigate various classes of two-dimensional spin models with long-range interactions at low temperatures. In particular, we study a dipolar XXZ model with U (1) symmetry that appears as a hard-core boson limit of an extended Hubbard model describing polarized dipolar atoms or molecules in an optical lattice. Tunneling, in such a model, is short-range, whereas density–density couplings decay with distance following a cubic power law. We also investigate an XXZ model with long-range couplings of all three spin components—such a model describes a system of ultracold ions in a lattice of microtraps. We describe an approximate phase diagram for such systems at zero and at finite temperature, and compare their properties. In particular, we compare the extent of crystalline, superfluid and supersolid phases. Our predictions apply directly to current experiments with mesoscopic numbers of polar molecules and trapped ions.

arXiv:1206.1752•New Journal of Physics•Nov 7, 2012•27 citations

The critical behaviour of the 1-dimensional XY model with power law decay long range interactions

Masahiro Takamoto, Yoshinori Muraoka, Toshihiro Idogaki

We discuss the critical behaviour of the 1-dimensional classical XY model with power law decay long range interactions by using Monte Carlo simulation. It has been predicted by renormalization group calculation that the critical behaviour changes with the power of interactions. From the simulation result of temperature dependence of the specific heat, we confirm that the system shows the critical behaviour of the mean field type and the non-trivial long range order. We also estimate the critical exponent η for the system with the inverse square long range interactions, and by using the phenomenological renormalization group plot, we confirm the 'Berezinskii-Kosterlitz-Thouless (BKT)-like' transition which has been predicted by the spin wave calculations.

Journal of Physics Conference Series•Jan 1, 2010•1 citation

Entanglement and fluctuations in the XXZ model with power-law interactions

Irénée Frérot, Piero Naldesi, Tommaso Roscilde

We investigate the ground-state properties of the spin-$1/2$ XXZ model with power-law-decaying ($1/{r}^{\ensuremath{\alpha}}$) interactions, which describe spins interacting with long-range transverse (XX) ferromagnetic interactions and longitudinal (Z) antiferromagnetic interactions, or hard-core bosons with long-range repulsion and hopping. The long-range nature of the couplings allows us to quantitatively study the spectral, correlation, and entanglement properties of the system by making use of linear spin-wave theory, supplemented with density-matrix renormalization group in one-dimensional systems. Our most important prediction is the existence of three distinct coupling regimes, depending on the decay exponent $\ensuremath{\alpha}$ and number of dimensions $d$: (1) a short-range regime for $\ensuremath{\alpha}>d+{\ensuremath{\sigma}}_{c}$ (where ${\ensuremath{\sigma}}_{c}=1$ in the gapped N\'eel antiferromagnetic phase exhibited by the XXZ model, and ${\ensuremath{\sigma}}_{c}=2$ in the gapless XY ferromagnetic phase), sharing the same properties as those of finite-range interactions ($\ensuremath{\alpha}=\ensuremath{\infty}$); (2) a long-range regime $\ensuremath{\alpha}<d$, sharing the same properties as those of the infinite-range interactions ($\ensuremath{\alpha}=0$) in the thermodynamic limit; and (3) a most intriguing medium-range regime for $d<\ensuremath{\alpha}<d+{\ensuremath{\sigma}}_{c}$, continuously interpolating between the finite-range and the infinite-range behavior. The latter regime is characterized by elementary excitations with a long-wavelength dispersion relation $\ensuremath{\omega}\ensuremath{\approx}{\mathrm{\ensuremath{\Delta}}}_{g}+c{k}^{z}$ in the gapped phase, and $\ensuremath{\omega}\ensuremath{\sim}{k}^{z}$ in the gapless phase, exhibiting a continuously varying dynamical exponent $z=(\ensuremath{\alpha}\ensuremath{-}d)/{\ensuremath{\sigma}}_{c}$. In the gapless phase of the model the $z$ exponent is found to control the scaling of fluctuations, the decay of correlations, and a universal subdominant term in the entanglement entropy, leading to a very rich palette of behaviors for ground-state quantum correlations beyond what is known for finite-range interactions.

arXiv:1703.01799•Physical review. B./Physical review. B•Jun 12, 2017•77 citations

Scale-invariant phase transition of disordered bosons in one dimension

Tanul Gupta, Guido Masella, Francesco Mattiotti +2 more

The disorder-induced quantum phase transition between superfluid and nonsuperfluid states of bosonic particles in one dimension is generally expected to be of the Berezinskii-Kosterlitz-Thouless (BKT) type. Here, we show that hard-core lattice bosons with power-law hopping decaying with distance as $1/{r}^{\ensuremath{\alpha}}$ with a finite integral over space---corresponding in spin language to an $XY$ model with power-law couplings---undergo a non-BKT continuous phase transition instead. We use exact quantum Monte Carlo methods to determine the phase diagram for different values of the exponent $\ensuremath{\alpha}$, focusing on the regime $\ensuremath{\alpha}>2$. We find that the scaling of the superfluid stiffness with the system size is scale invariant at the transition point for any $\ensuremath{\alpha}\ensuremath{\le}3$---a behavior incompatible with the BKT scenario and typical of continuous phase transitions in higher dimension. By a scaling analysis near the transition point, we find that our data are consistent with a correlation length exponent satisfying the Harris bound $\ensuremath{\nu}\ensuremath{\ge}2$ and demonstrate a universal behavior of disordered bosons in one dimension. For $\ensuremath{\alpha}>3$ our data are consistent with a BKT scenario where the liquid is pinned by infinitesimal disorder.

arXiv:2310.17682•Physical review. B./Physical review. B•Jan 8, 2025•3 citations

Continuous Symmetry Breaking in 1D Long-Range Interacting Quantum Systems

Mohammad F. Maghrebi, Zhexuan Gong, Alexey Vyacheslavovich Gorshkov

Continuous symmetry breaking (CSB) in low-dimensional systems, forbidden by the Mermin-Wagner theorem for short-range interactions, may take place in the presence of slowly decaying long-range interactions. Nevertheless, there is no stringent bound on how slowly interactions should decay to give rise to CSB in 1D quantum systems at zero temperature. Here, we study a long-range interacting spin chain with U(1) symmetry and power-law interactions V(r)∼1/r^{α}. Using a number of analytical and numerical techniques, we find CSB for α smaller than a critical exponent α_{c}(≤3) that depends on the microscopic parameters of the model. Furthermore, the transition from the gapless XY phase to the gapless CSB phase is mediated by the breaking of conformal and Lorentz symmetries due to long-range interactions, and is described by a universality class akin to, but distinct from, the Berezinskii-Kosterlitz-Thouless transition. Signatures of the CSB phase should be accessible in existing trapped-ion experiments.

arXiv:1510.01325•Physical Review Letters•Jul 11, 2017•128 citations
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 (1d1d1d) traps, these interactions decay as a power-law with distance 1/rα1/r^α1/rα, with a tunable exponent ααα. For small ααα, the resulting long-range 1d1d1d 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 αcα_cαc​ 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 1d1d1d XY model is enhanced in the long-range interacting regime. This is observed as a diverging superfluid density as α→0α\rightarrow 0α→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 αcα_cαc​.
We investigate the zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as 1/r^{α} using exact large scale quantum Monte Carlo simulations. For all 1<α≤3 the quantum phase transition from a superfluid and a Mott insulator at unit filling is found to be continuous and scale invariant, in marked contrast with the Berezinskii-Kosterlitz-Thouless (BKT) scenario that is recovered only for α>3. By performing finite-size scaling collapses of the superfluid stiffness and extracting dynamical and correlation-length exponents from the low-energy spectrum, we establish that these transitions define a distinct universality class throughout the long-range regime 1<α≤3. Analysis of the single-particle correlation functions and grand canonical phase diagram further reveals a sequence of ordering regimes within the superfluid phase: true long-range order for α≤2, anomalous quasi-long-range order for 2<α≤3, and conventional algebraic decay for α>3. Our exact numerical results provide a benchmark to compare theories of long-range quantum models and are relevant for experiments with cold neutral atom, molecules and ion chains.
We use a quantum Monte Carlo method to investigate various classes of two-dimensional spin models with long-range interactions at low temperatures. In particular, we study a dipolar XXZ model with U (1) symmetry that appears as a hard-core boson limit of an extended Hubbard model describing polarized dipolar atoms or molecules in an optical lattice. Tunneling, in such a model, is short-range, whereas density–density couplings decay with distance following a cubic power law. We also investigate an XXZ model with long-range couplings of all three spin components—such a model describes a system of ultracold ions in a lattice of microtraps. We describe an approximate phase diagram for such systems at zero and at finite temperature, and compare their properties. In particular, we compare the extent of crystalline, superfluid and supersolid phases. Our predictions apply directly to current experiments with mesoscopic numbers of polar molecules and trapped ions.
We discuss the critical behaviour of the 1-dimensional classical XY model with power law decay long range interactions by using Monte Carlo simulation. It has been predicted by renormalization group calculation that the critical behaviour changes with the power of interactions. From the simulation result of temperature dependence of the specific heat, we confirm that the system shows the critical behaviour of the mean field type and the non-trivial long range order. We also estimate the critical exponent η for the system with the inverse square long range interactions, and by using the phenomenological renormalization group plot, we confirm the 'Berezinskii-Kosterlitz-Thouless (BKT)-like' transition which has been predicted by the spin wave calculations.
We investigate the ground-state properties of the spin-1/21/21/2 XXZ model with power-law-decaying ($1/{r}^{\ensuremath{\alpha}}$) interactions, which describe spins interacting with long-range transverse (XX) ferromagnetic interactions and longitudinal (Z) antiferromagnetic interactions, or hard-core bosons with long-range repulsion and hopping. The long-range nature of the couplings allows us to quantitatively study the spectral, correlation, and entanglement properties of the system by making use of linear spin-wave theory, supplemented with density-matrix renormalization group in one-dimensional systems. Our most important prediction is the existence of three distinct coupling regimes, depending on the decay exponent $\ensuremath{\alpha}$ and number of dimensions ddd: (1) a short-range regime for $\ensuremath{\alpha}>d+{\ensuremath{\sigma}}_{c}$ (where ${\ensuremath{\sigma}}_{c}=1$ in the gapped N\'eel antiferromagnetic phase exhibited by the XXZ model, and ${\ensuremath{\sigma}}_{c}=2$ in the gapless XY ferromagnetic phase), sharing the same properties as those of finite-range interactions ($\ensuremath{\alpha}=\ensuremath{\infty}$); (2) a long-range regime $\ensuremath{\alpha}<d$, sharing the same properties as those of the infinite-range interactions ($\ensuremath{\alpha}=0$) in the thermodynamic limit; and (3) a most intriguing medium-range regime for $d<\ensuremath{\alpha}<d+{\ensuremath{\sigma}}_{c}$, continuously interpolating between the finite-range and the infinite-range behavior. The latter regime is characterized by elementary excitations with a long-wavelength dispersion relation $\ensuremath{\omega}\ensuremath{\approx}{\mathrm{\ensuremath{\Delta}}}_{g}+c{k}^{z}$ in the gapped phase, and $\ensuremath{\omega}\ensuremath{\sim}{k}^{z}$ in the gapless phase, exhibiting a continuously varying dynamical exponent $z=(\ensuremath{\alpha}\ensuremath{-}d)/{\ensuremath{\sigma}}_{c}$. In the gapless phase of the model the zzz exponent is found to control the scaling of fluctuations, the decay of correlations, and a universal subdominant term in the entanglement entropy, leading to a very rich palette of behaviors for ground-state quantum correlations beyond what is known for finite-range interactions.
The disorder-induced quantum phase transition between superfluid and nonsuperfluid states of bosonic particles in one dimension is generally expected to be of the Berezinskii-Kosterlitz-Thouless (BKT) type. Here, we show that hard-core lattice bosons with power-law hopping decaying with distance as $1/{r}^{\ensuremath{\alpha}}$ with a finite integral over space---corresponding in spin language to an XYXYXY model with power-law couplings---undergo a non-BKT continuous phase transition instead. We use exact quantum Monte Carlo methods to determine the phase diagram for different values of the exponent $\ensuremath{\alpha}$, focusing on the regime $\ensuremath{\alpha}>2$. We find that the scaling of the superfluid stiffness with the system size is scale invariant at the transition point for any $\ensuremath{\alpha}\ensuremath{\le}3$---a behavior incompatible with the BKT scenario and typical of continuous phase transitions in higher dimension. By a scaling analysis near the transition point, we find that our data are consistent with a correlation length exponent satisfying the Harris bound $\ensuremath{\nu}\ensuremath{\ge}2$ and demonstrate a universal behavior of disordered bosons in one dimension. For $\ensuremath{\alpha}>3$ our data are consistent with a BKT scenario where the liquid is pinned by infinitesimal disorder.
Continuous symmetry breaking (CSB) in low-dimensional systems, forbidden by the Mermin-Wagner theorem for short-range interactions, may take place in the presence of slowly decaying long-range interactions. Nevertheless, there is no stringent bound on how slowly interactions should decay to give rise to CSB in 1D quantum systems at zero temperature. Here, we study a long-range interacting spin chain with U(1) symmetry and power-law interactions V(r)∼1/r^{α}. Using a number of analytical and numerical techniques, we find CSB for α smaller than a critical exponent α_{c}(≤3) that depends on the microscopic parameters of the model. Furthermore, the transition from the gapless XY phase to the gapless CSB phase is mediated by the breaking of conformal and Lorentz symmetries due to long-range interactions, and is described by a universality class akin to, but distinct from, the Berezinskii-Kosterlitz-Thouless transition. Signatures of the CSB phase should be accessible in existing trapped-ion experiments.