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arxiv: 2502.20759 · v1 · submitted 2025-02-28 · ❄️ cond-mat.quant-gas · quant-ph

Efimov Effect in Long-range Quantum Spin Chains

Ning Sun , Lei Feng , Pengfei Zhang This is my paper

Pith reviewed 2026-05-23 02:22 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas quant-ph
keywords Efimov effectlong-range quantum spin chainsmagnon dispersionscale invariancebound stateseffective field theorytrapped ions
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The pith

Long-range coupling in quantum spin chains produces the Efimov effect through modified magnon dispersion and broken scale invariance.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that the Efimov effect, with its infinite tower of three-body bound states showing discrete scale invariance, appears in long-range quantum spin chains. Long-range coupling alters the low-energy dispersion of magnons to produce continuous scale invariance for resonant two-magnon states. Imposing short-range boundary conditions on the three-magnon problem breaks this invariance to discrete form and generates the bound states. Effective field theory yields the ratio of successive binding energies as a function of interaction range, matching numerical solutions, and the results extend to arbitrary dimensions with possible tests in trapped-ion systems.

Core claim

The long-range coupling modifies the low-energy dispersion of magnons, enabling the emergence of continuous scale invariance for two-magnon states at resonance. This invariance is subsequently broken to discrete scale invariance upon imposing short-range boundary conditions for the three-magnon problem, leading to the Efimov bound states. Using effective field theory, the ratio of two successive binding energies is determined as a function of the interaction range and agrees with the numerical solution of the bound-state problem.

What carries the argument

Long-range coupling that alters magnon dispersion to support continuous scale invariance at two-magnon resonance, broken to discrete invariance by short-range boundary conditions in the three-magnon sector.

If this is right

  • The ratio of two successive Efimov binding energies depends on the interaction range.
  • The Efimov effect generalizes to arbitrary spatial dimensions, with the standard three-dimensional case as a special instance.
  • Universal physics emerges in dilute quantum gases of magnons.
  • The effect can be tested experimentally in trapped-ion systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Long-range interactions may induce analogous scale-invariance effects in other condensed-matter few-body systems.
  • Adjusting the range parameter could provide experimental control over Efimov ratios beyond short-range cases.
  • The approach suggests new routes to engineer discrete scale invariance in quantum simulators.

Load-bearing premise

Short-range boundary conditions can be imposed for the three-magnon problem while the two-magnon sector retains continuous scale invariance purely from the long-range coupling.

What would settle it

Numerical solution of the three-magnon bound-state problem yielding binding-energy ratios that differ from the effective-field-theory prediction for a chosen interaction range.

Figures

Figures reproduced from arXiv: 2502.20759 by Lei Feng, Ning Sun, Pengfei Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. We present a schematic of our main results. We [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) The self-energy diagram of the dimer field [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The theoretical prediction of the scale factor for [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
read the original abstract

When two non-relativistic particles interact resonantly in three dimensions, an infinite tower of three-body bound states emerges, exhibiting a discrete scale invariance. This universal phenomenon, known as the Efimov effect, has garnered extensive attention across various fields, including atomic, nuclear, condensed matter, and particle physics. In this letter, we demonstrate that the Efimov effect also manifests in long-range quantum spin chains. The long-range coupling modifies the low-energy dispersion of magnons, enabling the emergence of continuous scale invariance for two-magnon states at resonance. This invariance is subsequently broken to discrete scale invariance upon imposing short-range boundary conditions for the three-magnon problem, leading to the celebrated Efimov bound states. Using effective field theory, we theoretically determine how the ratio of two successive binding energies depends on the interaction range, which agrees with the numerical solution of the bound-state problem. We further discuss generalizations to arbitrary spatial dimensions, where the traditional Efimov effect serves as a special case. Our results reveal universal physics in dilute quantum gases of magnons that can be experimentally tested in trapped-ion systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that long-range couplings in quantum spin chains modify the low-energy magnon dispersion, producing continuous scale invariance for resonant two-magnon states; imposing short-range boundary conditions on the three-magnon sector then breaks this to discrete scale invariance, yielding Efimov bound states. Effective field theory is used to derive the dependence of the ratio of successive binding energies on the interaction range, which is reported to agree with numerical solutions of the bound-state problem. Generalizations to arbitrary spatial dimensions are discussed, with the conventional Efimov effect recovered as a special case.

Significance. If the central construction is valid, the work identifies a condensed-matter realization of the Efimov effect in dilute magnon gases, with the range dependence of the binding-energy ratio and the dimensional generalizations providing concrete extensions beyond the standard three-dimensional case. Potential experimental accessibility in trapped-ion systems is noted as a strength.

major comments (2)
  1. [Sections describing the two- and three-magnon effective theories and boundary conditions] The load-bearing separation between sectors: the two-magnon problem is treated with purely long-range dispersion to obtain continuous scale invariance at resonance, while the three-magnon problem receives independent short-range boundary conditions that break the invariance. The manuscript must explicitly justify this construction, because the underlying spin-chain Hamiltonian is long-range for all particles; without an auxiliary short-range term whose strength is tuned separately, the same interaction governs both sectors and the boundary-condition split is not automatic.
  2. [Effective field theory derivation and numerical comparison sections] The agreement between EFT and numerics for the binding-energy ratio is stated in the abstract, but the derivation of the ratio as a function of range (including any fitting or parameter choices) and the error analysis on the numerical solutions are not verifiable from the provided material; this directly affects whether the ratio is parameter-free or contains post-hoc adjustments.
minor comments (1)
  1. Notation for the interaction range parameter and the magnon dispersion relation should be introduced consistently in the main text before being used in equations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments, which help clarify the presentation of our results on the Efimov effect in long-range spin chains. We address the major comments below and will incorporate revisions as indicated.

read point-by-point responses

  1. Referee: [Sections describing the two- and three-magnon effective theories and boundary conditions] The load-bearing separation between sectors: the two-magnon problem is treated with purely long-range dispersion to obtain continuous scale invariance at resonance, while the three-magnon problem receives independent short-range boundary conditions that break the invariance. The manuscript must explicitly justify this construction, because the underlying spin-chain Hamiltonian is long-range for all particles; without an auxiliary short-range term whose strength is tuned separately, the same interaction governs both sectors and the boundary-condition split is not automatic.

    Authors: The two-magnon sector is solved directly from the long-range spin-chain Hamiltonian, yielding the modified dispersion that permits a resonant condition with continuous scale invariance. In the three-magnon sector the same long-range interaction is retained at long distances, but the short-distance boundary condition is fixed by the ultraviolet cutoff of the effective theory (where the lattice discreteness and higher-order terms dominate). This construction follows the standard separation in Efimov physics between the infrared resonant two-body physics and the short-distance three-body parameter. We agree the manuscript should state this separation more explicitly and will add a dedicated paragraph in the revised version deriving the boundary condition from the underlying Hamiltonian. revision: yes

  2. Referee: [Effective field theory derivation and numerical comparison sections] The agreement between EFT and numerics for the binding-energy ratio is stated in the abstract, but the derivation of the ratio as a function of range (including any fitting or parameter choices) and the error analysis on the numerical solutions are not verifiable from the provided material; this directly affects whether the ratio is parameter-free or contains post-hoc adjustments.

    Authors: The ratio is obtained analytically within the EFT by solving the renormalization-group equation for the three-body coupling with the range-dependent two-body scattering length; no numerical fitting enters the functional form. The numerical bound-state solutions are obtained by solving the three-body integral equation with the long-range kernel. We acknowledge that the explicit steps, parameter choices, and error estimates are not fully detailed in the letter format. In the revision we will add an appendix containing the closed-form expression for the ratio, the numerical method, convergence checks, and error bars on the data points to demonstrate that the comparison is parameter-free within the stated approximations. revision: yes

Circularity Check

0 steps flagged

No circularity; EFT derivation checked against independent numerics

full rationale

The paper derives the binding-energy ratio from effective field theory applied to the long-range-modified magnon dispersion (continuous scale invariance for two magnons) plus imposed short-range boundary conditions (discrete scale invariance for three magnons). This ratio is then compared to a separate numerical solution of the bound-state problem. No quoted step reduces a claimed prediction to a fitted input by construction, nor does any load-bearing premise rest solely on self-citation. The separation of boundary conditions is a modeling assumption whose validity is external to the derivation chain itself and is not circular.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no specific free parameters, axioms, or invented entities can be identified from the text. The approach relies on standard effective field theory and numerical methods whose details are not provided.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Universal Relations in Long-range Quantum Spin Chains

    cond-mat.quant-gas 2025-10 unverdicted novelty 7.0

    Universal relations connect asymptotic equal-time spin correlations, dynamical structure factor, and contact density in long-range quantum spin chains via effective field theory and operator product expansion, with nu...

Reference graph

Works this paper leans on

77 extracted references · 77 canonical work pages · cited by 1 Pith paper · 9 internal anchors

  1. [1]

    L. D. Landau and E. M. Lifshitz, Quantum mechanics: non-relativistic theory, Vol. 3 (Elsevier, 2013)

    work page 2013

  2. [2]

    Efimov, Energy levels arising from resonant two-body forces in a three-body system, Physics Letters B 33, 563 (1970)

    V. Efimov, Energy levels arising from resonant two-body forces in a three-body system, Physics Letters B 33, 563 (1970)

    work page 1970

  3. [3]

    H. W. Hammer, Universality in few-body systems with large scattering length, AIP Conf. Proc. 777, 1 (2005), arXiv:nucl-th/0502080

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  4. [4]

    Nielsen, D

    E. Nielsen, D. V. Fedorov, A. S. Jensen, and E. Garrido, The three-body problem with short-range interactions, Phys. Rept. 347, 373 (2001)

    work page 2001

  5. [5]

    Ferlaino and R

    F. Ferlaino and R. Grimm, Forty years of efimov physics: How a bizarre prediction turned into a hot topic, Physics 3, 9 (2010)

    work page 2010

  6. [6]

    Braaten and H

    E. Braaten and H. W. Hammer, Efimov Physics in Cold Atoms, Annals Phys. 322, 120 (2007), arXiv:cond- mat/0612123

    work page arXiv 2007

  7. [7]

    Efimov States in Nuclear and Particle Physics

    H.-W. Hammer and L. Platter, Efimov States in Nuclear and Particle Physics, Ann. Rev. Nucl. Part. Sci. 60, 207 (2010), arXiv:1001.1981 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  8. [8]

    Efimov effect in quantum magnets

    Y. Nishida, Y. Kato, and C. D. Batista, Efimov ef- fect in quantum magnets, Nature Phys. 9, 93 (2013), arXiv:1208.6214 [cond-mat.str-el]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  9. [9]

    Naidon and S

    P. Naidon and S. Endo, Efimov Physics: a review, Rept. Prog. Phys. 80, 056001 (2017), arXiv:1610.09805 [quant- ph]

    work page arXiv 2017

  10. [10]

    H. Wang, H. Liu, Y. Li, Y. Liu, J. Wang, J. Liu, J.-Y. Dai, Y. Wang, L. Li, J. Yan, D. Man- drus, X. C. Xie, and J. Wang, Discovery of log- periodic oscillations in ultraquantum topological materials, Science Advances 4, eaau5096 (2018), https://www.science.org/doi/pdf/10.1126/sciadv.aau5096

    work page doi:10.1126/sciadv.aau5096 2018

  11. [11]

    Kievsky, L

    A. Kievsky, L. Girlanda, M. Gattobigio, and M. Vi- viani, Efimov Physics and Connections to Nuclear Physics, Ann. Rev. Nucl. Part. Sci. 71, 465 (2021), arXiv:2102.13504 [nucl-th]

    work page arXiv 2021

  12. [12]

    Zhang and H

    P. Zhang and H. Zhai, Scaling symmetry meets topology, Science Bulletin 64, 289 (2019)

    work page 2019

  13. [13]

    Evidence for Efimov quantum states in an ultracold gas of cesium atoms

    T. Kraemer, M. Mark, P. Waldburger, J. G. Danzl, C. Chin, B. Engeser, A. D. Lange, K. Pilch, A. Jaakkola, H. C. N¨ agerl, and R. Grimm, Evidence for Efimov quan- tum states in an ultracold gas of caesium atoms, Na- ture (London) 440, 315 (2006), arXiv:cond-mat/0512394 [cond-mat.other]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  14. [14]

    Huang, L

    B. Huang, L. A. Sidorenkov, R. Grimm, and J. M. Hut- son, Observation of the second triatomic resonance in efimov’s scenario, Phys. Rev. Lett. 112, 190401 (2014)

    work page 2014

  15. [15]

    Pires, J

    R. Pires, J. Ulmanis, S. H¨ afner, M. Repp, A. Arias, E. D. Kuhnle, and M. Weidem¨ uller, Observation of efimov reso- nances in a mixture with extreme mass imbalance, Phys. Rev. Lett. 112, 250404 (2014)

    work page 2014

  16. [16]

    S.-K. Tung, K. Jim´ enez-Garc´ ıa, J. Johansen, C. V. Parker, and C. Chin, Geometric scaling of efimov states in a 6Li−133Cs mixture, Phys. Rev. Lett. 113, 240402 (2014)

    work page 2014

  17. [17]

    Kunitski, S

    M. Kunitski, S. Zeller, J. Voigtsberger, A. Kalinin, L. P. H. Schmidt, M. Sch¨ offler, A. Czasch, W. Sch¨ ollkopf, R. E. Grisenti, T. Jahnke, D. Blume, and R. D¨ orner, Observation of the efimov state of the helium trimer, Science 348, 551 (2015), https://www.science.org/doi/pdf/10.1126/science.aaa5601

    work page doi:10.1126/science.aaa5601 2015

  18. [18]

    Liberating Efimov physics from three dimensions

    Y. Nishida and S. Tan, Liberating Efimov physics from three dimensions, Few Body Syst. 51, 191 (2011), arXiv:1104.2387 [cond-mat.quant-gas]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  19. [19]

    Nishida and S

    Y. Nishida and S. Tan, Universal fermi gases in mixed dimensions, Phys. Rev. Lett. 101, 170401 (2008)

    work page 2008

  20. [20]

    Nishida and S

    Y. Nishida and S. Tan, Confinement-induced efimov reso- nances in fermi-fermi mixtures, Phys. Rev. A 79, 060701 (2009)

    work page 2009

  21. [21]

    Wu and L.-M

    Y.-K. Wu and L.-M. Duan, Research progress of ion trap quantum computing, ACTA PHYSICA SINICA 72 (2023)

    work page 2023

  22. [22]

    C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, Trapped-ion quantum computing: Progress and challenges, Applied Physics Reviews 6, 021314 (2019), arXiv:1904.04178 [quant-ph]

    work page arXiv 2019

  23. [23]

    Foss-Feig, G

    M. Foss-Feig, G. Pagano, A. C. Potter, and N. Y. Yao, Progress in Trapped-Ion Quantum Simulation, (2024), arXiv:2409.02990 [quant-ph]

    work page arXiv 2024

  24. [24]

    K. R. Brown, J. Chiaverini, J. M. Sage, and H. H¨ affner, Materials challenges for trapped-ion quantum com- puters, Nature Reviews Materials 6, 892 (2021), arXiv:2009.00568 [quant-ph]

    work page arXiv 2021

  25. [25]

    Castillo, The electronic control system of a trapped- ion quantum processor: A systematic literature review, IEEE Access 11, 65775 (2023)

    S. Castillo, The electronic control system of a trapped- ion quantum processor: A systematic literature review, IEEE Access 11, 65775 (2023)

    work page 2023

  26. [26]

    Monroe, W

    C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, P. Richerme, C. Senko, and N. Y. Yao, Programmable quantum simulations of spin systems with trapped ions, Rev. Mod. Phys. 93, 025001 (2021)

    work page 2021

  27. [27]

    S. J. Evered, D. Bluvstein, M. Kalinowski, S. Ebadi, T. Manovitz, H. Zhou, S. H. Li, A. A. Geim, T. T. Wang, N. Maskara, H. Levine, G. Semeghini, M. Greiner, V. Vuleti´ c, and M. D. Lukin, High-fidelity parallel entan- gling gates on a neutral-atom quantum computer, Nature 622, 268 (2023)

    work page 2023

  28. [28]

    S. Ma, G. Liu, P. Peng, B. Zhang, S. Jandura, J. Claes, A. P. Burgers, G. Pupillo, S. Puri, and J. D. Thompson, High-fidelity gates and mid-circuit erasure conversion in an atomic qubit, Nature 622, 279 (2023)

    work page 2023

  29. [29]

    Bluvstein, S

    D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kali- nowski, D. Hangleiter, J. P. Bonilla Ataides, N. Maskara, I. Cong, X. Gao, P. Sales Rodriguez, T. Karolyshyn, G. Semeghini, M. J. Gullans, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Logical quantum processor based on reconfigurable atom arrays, Nature 626, ...

    work page 2024

  30. [30]

    Bekenstein, I

    R. Bekenstein, I. Pikovski, H. Pichler, E. Shahmoon, S. F. Yelin, and M. D. Lukin, Quantum metasurfaces with atom arrays, Nature Physics 16, 676 (2020)

    work page 2020

  31. [31]

    Bluvstein, A

    D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Se- 6 meghini, S. Ebadi, T. T. Wang, A. A. Michailidis, N. Maskara, W. W. Ho, S. Choi, M. Serbyn, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Controlling quantum many- body dynamics in driven rydberg atom arrays, Science 371, 1355 (2021)

    work page 2021

  32. [32]

    Ebadi, A

    S. Ebadi, A. Keesling, M. Cain, T. T. Wang, H. Levine, D. Bluvstein, G. Semeghini, A. Omran, J. G. Liu, R. Samajdar, X. Z. Luo, B. Nash, X. Gao, B. Barak, E. Farhi, S. Sachdev, N. Gemelke, L. Zhou, S. Choi, H. Pichler, S. T. Wang, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Quantum optimization of maximum independent set using rydberg atom arrays, Science ...

    work page 2022

  33. [33]

    Bluvstein, H

    D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner, V. Vuleti´ c, and M. D. Lukin, A quantum processor based on coherent transport of en- tangled atom arrays, Nature 604, 451 (2022)

    work page 2022

  34. [34]

    J. W. Lis, A. Senoo, W. F. McGrew, F. R¨ onchen, A. Jenkins, and A. M. Kaufman, Midcircuit operations using the omg architecture in neutral atom arrays, Phys- ical Review X 13, 041035 (2023)

    work page 2023

  35. [35]

    H. J. Manetsch, G. Nomura, E. Bataille, K. H. Leung, X. Lv, and M. Endres, A tweezer array with 6100 highly coherent atomic qubits (2024)

    work page 2024

  36. [36]

    R. Tao, M. Ammenwerth, F. Gyger, I. Bloch, and J. Zei- her, High-fidelity detection of large-scale atom arrays in an optical lattice, Physical Review Letters 133, 013401 (2024)

    work page 2024

  37. [37]

    A. Cao, W. J. Eckner, T. Lukin Yelin, A. W. Young, S. Jandura, L. Yan, K. Kim, G. Pupillo, J. Ye, N. Dark- wah Oppong, and A. M. Kaufman, Multi-qubit gates and schr¨ odinger cat states in an optical clock, Nature 634, 315 (2024)

    work page 2024

  38. [38]

    Jones, Nmr quantum computation, Progress in Nuclear Magnetic Resonance Spectroscopy 38, 325 (2001)

    J. Jones, Nmr quantum computation, Progress in Nuclear Magnetic Resonance Spectroscopy 38, 325 (2001)

    work page 2001

  39. [39]

    L. M. K. Vandersypen and I. L. Chuang, Nmr techniques for quantum control and computation, Rev. Mod. Phys. 76, 1037 (2005)

    work page 2005

  40. [40]

    D. Lu, A. Brodutch, J. Park, H. Katiyar, T. Jochym- O’Connor, and R. Laflamme, Nmr quantum information processing, arXiv: Quantum Physics , 193 (2015)

    work page 2015

  41. [41]

    D. G. Cory, R. Laflamme, E. Knill, L. Viola, T. F. Havel, N. Boulant, G. S. Boutis, E. M. Fortunato, S. Lloyd, R. Martinez, C. Negrevergne, M. A. Pravia, Y. Sharf, G. Teklemariam, Y. S. Weinstein, and W. H. Zurek, Nmr based quantum information processing: Achievements and prospects, Protein Science 48, 875 (2000)

    work page 2000

  42. [42]

    Laflamme, E

    R. Laflamme, E. Knill, D. G. Cory, E. M. Fortunato, T. F. Havel, C. Miquel, R. Martinez, C. Negrevergne, G. Ortiz, M. A. Pravia, Y. Sharf, S. Sinha, R. D. Somma, and L. Viola, Introduction to nmr quantum information processing, arXiv: Quantum Physics (2002)

    work page 2002

  43. [43]

    K. Kim, M. S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G. D. Lin, L. M. Duan, and C. Monroe, Quantum simulation of frustrated Ising spins with trapped ions, Nature 465, 590 (2010)

    work page 2010

  44. [44]

    Monroe et al

    C. Monroe et al. , Quantum simulation of the transverse Ising model with trapped ions, New J. Phys. 13, 105003 (2011)

    work page 2011

  45. [45]

    Schneider, D

    C. Schneider, D. Porras, and T. Schaetz, Experimental quantum simulations of many-body physics with trapped ions, Reports on Progress in Physics 75, 024401 (2012)

    work page 2012

  46. [46]

    Bermudez, T

    A. Bermudez, T. Schaetz, and D. Porras, Synthetic gauge fields for vibrational excitations of trapped ions, Phys. Rev. Lett. 107, 150501 (2011)

    work page 2011

  47. [47]

    P. T. Dumitrescu, J. G. Bohnet, J. P. Gaebler, A. Han- kin, D. Hayes, A. Kumar, B. Neyenhuis, R. Vasseur, and A. C. Potter, Dynamical topological phase realized in a trapped-ion quantum simulator, Nature 607, 463 (2022), arXiv:2107.09676 [quant-ph]

    work page arXiv 2022

  48. [48]

    Morong, F

    W. Morong, F. Liu, P. Becker, K. S. Collins, L. Feng, A. Kyprianidis, G. Pagano, T. You, A. V. Gorshkov, and C. Monroe, Publisher Correction: Observation of Stark many-body localization without disorder [doi: 10.1038/s41586-021-03988-0], Nature 599, 393 (2021), arXiv:2102.07250 [quant-ph]

    work page doi:10.1038/s41586-021-03988-0 2021

  49. [49]

    Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator

    J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z. X. Gong, and C. Monroe, Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator, Nature 551, 601 (2017), arXiv:1708.01044 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  50. [50]

    M. K. Joshi, F. Kranzl, A. Schuckert, I. Lovas, C. Maier, R. Blatt, M. Knap, and C. F. Roos, Observing emergent hydrodynamics in a long-range quantum magnet, Science 376, 720 (2022), arXiv:2107.00033 [quant-ph]

    work page arXiv 2022

  51. [51]

    Lepori, D

    L. Lepori, D. Vodola, G. Pupillo, G. Gori, and A. Trom- bettoni, Effective theory and breakdown of conformal symmetry in a long-range quantum chain, Annals of Physics 374, 35 (2016)

    work page 2016

  52. [52]

    Viyuela, D

    O. Viyuela, D. Vodola, G. Pupillo, and M. A. Martin- Delgado, Topological massive dirac edge modes and long- range superconducting hamiltonians, Phys. Rev. B 94, 125121 (2016)

    work page 2016

  53. [53]

    Jiang, J

    S.-J. Jiang, J. Maki, and F. Zhou, Long-lived universal resonant bose gases, Phys. Rev. A 93, 043605 (2016)

    work page 2016

  54. [54]

    See supplementary material for: (1) the two-body prob- lem of the microscopic Hamiltonian, (2) the analysis for generic dimension D

    work page

  55. [55]

    Zhai, Ultracold atomic physics (Cambridge University Press, 2021)

    H. Zhai, Ultracold atomic physics (Cambridge University Press, 2021)

    work page 2021

  56. [56]

    P. F. Bedaque, H. W. Hammer, and U. van Kolck, Renor- malization of the three-body system with short range in- teractions, Phys. Rev. Lett. 82, 463 (1999), arXiv:nucl- th/9809025

    work page arXiv 1999

  57. [57]

    P. F. Bedaque, H. W. Hammer, and U. van Kolck, The Three boson system with short range interactions, Nucl. Phys. A 646, 444 (1999), arXiv:nucl-th/9811046

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  58. [58]

    G. V. Skorniakov and K. A. Ter-Martirosian, Three Body Problem for Short Range Forces. I. Scattering of Low Energy Neutrons by Deuterons, Sov. Phys. JETP 4, Sov.Phys.JETP (1957)

    work page 1957

  59. [59]

    Here, we focus on the even-wave solution between magnon and dimer

    work page

  60. [60]

    D. H. Smith, E. Braaten, D. Kang, and L. Platter, Two- body and three-body contacts for identical bosons near unitarity, Phys. Rev. Lett. 112, 110402 (2014)

    work page 2014

  61. [61]

    Braaten, D

    E. Braaten, D. Kang, and L. Platter, Universal relations for identical bosons from three-body physics, Phys. Rev. Lett. 106, 153005 (2011)

    work page 2011

  62. [62]

    Werner and Y

    F. Werner and Y. Castin, General relations for quantum gases in two and three dimensions. ii. bosons and mix- tures, Phys. Rev. A 86, 053633 (2012)

    work page 2012

  63. [63]

    Nishida, S

    Y. Nishida, S. Moroz, and D. T. Son, Super efimov ef- fect of resonantly interacting fermions in two dimensions, Phys. Rev. Lett. 110, 235301 (2013)

    work page 2013

  64. [64]

    Moroz and Y

    S. Moroz and Y. Nishida, Super efimov effect for mass- imbalanced systems, Phys. Rev. A 90, 063631 (2014)

    work page 2014

  65. [65]

    D. K. Gridnev, Proof of the Super Efimov Effect, arXiv e- 7 prints , arXiv:1405.1787 (2014), arXiv:1405.1787 [math- ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  66. [66]

    C. Gao, J. Wang, and Z. Yu, Revealing the origin of super efimov states in the hyperspherical formalism, Phys. Rev. A 92, 020504 (2015)

    work page 2015

  67. [67]

    Zhang and Z

    P. Zhang and Z. Yu, Signature of the universal super efi- mov effect: Three-body contact in two-dimensional fermi gases, Phys. Rev. A 95, 033611 (2017)

    work page 2017

  68. [68]

    Nishida, Semisuper efimov effect of two-dimensional bosons at a three-body resonance, Phys

    Y. Nishida, Semisuper efimov effect of two-dimensional bosons at a three-body resonance, Phys. Rev. Lett. 118, 230601 (2017)

    work page 2017

  69. [69]

    Zhang and Z

    P. Zhang and Z. Yu, Universal three-body bound states in mixed dimensions beyond the efimov paradigm, Phys. Rev. A 96, 030702 (2017)

    work page 2017

  70. [70]

    Tan, Large momentum part of a strongly correlated fermi gas, Annals of Physics 323, 2971 (2008)

    S. Tan, Large momentum part of a strongly correlated fermi gas, Annals of Physics 323, 2971 (2008)

    work page 2008

  71. [71]

    Braaten and L

    E. Braaten and L. Platter, Exact relations for a strongly interacting fermi gas from the operator product expan- sion, Phys. Rev. Lett. 100, 205301 (2008)

    work page 2008

  72. [72]

    G. Baym, C. J. Pethick, Z. Yu, and M. W. Zwierlein, Co- herence and clock shifts in ultracold fermi gases with res- onant interactions, Phys. Rev. Lett. 99, 190407 (2007)

    work page 2007

  73. [73]

    Punk and W

    M. Punk and W. Zwerger, Theory of rf-spectroscopy of strongly interacting fermions, Phys. Rev. Lett. 99, 170404 (2007)

    work page 2007

  74. [74]

    M. He, S. Zhang, H. M. Chan, and Q. Zhou, Concept of a contact spectrum and its applications in atomic quantum hall states, Phys. Rev. Lett. 116, 045301 (2016)

    work page 2016

  75. [75]

    Number of closed-channel molecules in the BEC-BCS crossover

    F. Werner, L. Tarruell, and Y. Castin, Number of closed- channel molecules in the BEC-BCS crossover, Euro- pean Physical Journal B 68, 401 (2009), arXiv:0807.0078 [cond-mat.other]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  76. [76]

    Combescot, F

    R. Combescot, F. Alzetto, and X. Leyronas, Particle dis- tribution tail and related energy formula, Phys. Rev. A 79, 053640 (2009)

    work page 2009

  77. [77]

    Zhang and A

    S. Zhang and A. J. Leggett, Universal properties of the ultracold fermi gas, Phys. Rev. A 79, 023601 (2009). Supplementary material: Efimov Effect in Long-range Quantum Spin Chains Ning Sun, 1 Lei Feng, 1, 2, ∗ and Pengfei Zhang 1, 2, 3, 4, † 1Department of Physics, Fudan University, Shanghai, 200438, China 2State Key Laboratory of Surface Physics, Fudan Un...

    work page 2009