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Quantum-critical and dynamical properties of the XXZ bilayer with long-range interactions
Strongly Correlated Electrons · Submitted 23 Aug 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Along the decay exponent axis, we demonstrate mean-field behavior for strong long-range couplings, the aforementioned three universality classes for sufficiently weak interactions, and continuously varying critical exponents in-between.
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The abstract, sentence by sentence
We study the XXZ square lattice bilayer model with antiferromagnetic non-frustrating long-range interactions that decay as a power law with the distance. Employing large-scale high-order series expansions with classical Monte Carlo integration (pCUT+MC) about the limit of isolated Heisenberg dimers in the rung-singlet phase, we investigate the one-triplon dispersion and the corresponding spectral weight along the parameter axes of the long-range decay exponent and the XXZ anisotropy. By tuning the latter, we observe two extended regions of 3d XY and Ising universality as well as 3d Heisenberg critical exponents at the isotropic point. Along the decay exponent axis, we demonstrate mean-field behavior for strong long-range couplings, the aforementioned three universality classes for sufficiently weak interactions, and continuously varying critical exponents in-between. Using extrapolations we are able to determine the one-triplon dispersion in a quantitative fashion up to the quantum-critical breakdown of the rung-singlet phase. This allows to extract the dynamical critical exponent $z$ as a function of the decay exponent, displaying a universal behavior. The detected $z<1$ for small decay exponents is in agreement with the expected properties of the anomalous Goldstone modes in the ordered phases with broken continuous symmetry.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the XXZ square lattice bilayer model with antiferromagnetic non-frustrating long-range interactions that decay as a power law with the distance. | contribution 0.76 | 0.58 | 0.03 | asserted 0.88 |
| s1 | Employing large-scale high-order series expansions with classical Monte Carlo integration (pCUT+MC) about the limit of isolated Heisenberg dimers in the rung-singlet phase, we investigate the one-triplon dispersion and the corresponding spectral weight along the parameter axes of the long-range decay exponent and the XXZ anisotropy. | method 0.95 | 0.95 | 0.05 | asserted 0.92 |
| s2 | By tuning the latter, we observe two extended regions of 3d XY and Ising universality as well as 3d Heisenberg critical exponents at the isotropic point. | result 1.00 | 0.95 | 0.18 | asserted 1.00 |
| s3 | Along the decay exponent axis, we demonstrate mean-field behavior for strong long-range couplings, the aforementioned three universality classes for sufficiently weak interactions, and continuously varying critical exponents in-between. | result 1.00 | 0.96 | 0.25 | asserted 1.00 |
| s4 | Using extrapolations we are able to determine the one-triplon dispersion in a quantitative fashion up to the quantum-critical breakdown of the rung-singlet phase. | result 0.53 | 0.96 | 0.13 | asserted 0.99 |
| s5 | This allows to extract the dynamical critical exponent $z$ as a function of the decay exponent, displaying a universal behavior. | result 0.95 | 0.94 | 0.21 | asserted 1.00 |
| s6 | The detected $z<1$ for small decay exponents is in agreement with the expected properties of the anomalous Goldstone modes in the ordered phases with broken continuous symmetry. | interpretation 0.93 | 0.87 | 0.14 | asserted 0.58 |
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Original abstract
We study the XXZ square lattice bilayer model with antiferromagnetic non-frustrating long-range interactions that decay as a power law with the distance. Employing large-scale high-order series expansions with classical Monte Carlo integration (pCUT+MC) about the limit of isolated Heisenberg dimers in the rung-singlet phase, we investigate the one-triplon dispersion and the corresponding spectral weight along the parameter axes of the long-range decay exponent and the XXZ anisotropy. By tuning the latter, we observe two extended regions of 3d XY and Ising universality as well as 3d Heisenberg critical exponents at the isotropic point. Along the decay exponent axis, we demonstrate mean-field behavior for strong long-range couplings, the aforementioned three universality classes for sufficiently weak interactions, and continuously varying critical exponents in-between. Using extrapolations we are able to determine the one-triplon dispersion in a quantitative fashion up to the quantum-critical breakdown of the rung-singlet phase. This allows to extract the dynamical critical exponent $z$ as a function of the decay exponent, displaying a universal behavior. The detected $z<1$ for small decay exponents is in agreement with the expected properties of the anomalous Goldstone modes in the ordered phases with broken continuous symmetry.
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Staggered tunable-range interactions have been studied previously for the Heisenberg model [ref] .
First- and second-order quantum phase transitions in the long-range unfrustrated antiferromagnetic Ising chain · The model · 0.94
What it cites · 4 sentences without a confident label
Cites as background 2 papers
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Often, the long-range transverse-field Ising model (LRTFIM), which possesses a discrete symmetry, served as a paradigmatic model for numerical techniques to study the quantum-critical behavior of long-range quantum systems [ref] probing field-theoretical predictions from the long-range $O(n)$ quantum rotor model [ref] and to study the intriguing interplay of long-range interactions and frustration [ref] .
Stochastic parameter optimization analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain · Introduction · 0.85
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Often, the long-range transverse-field Ising model (LRTFIM), which possesses a discrete symmetry, served as a paradigmatic model for numerical techniques to study the quantum-critical behavior of long-range quantum systems [ref] probing field-theoretical predictions from the long-range $O(n)$ quantum rotor model [ref] and to study the intriguing interplay of long-range interactions and frustration [ref] .
Order-by-disorder in the antiferromagnetic $J_1$-$J_2$-$J_3$ transverse-field Ising model on the ruby lattice · Introduction · 0.85
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