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Detection of a Rényi Index Dependent Transition in Entanglement Entropy Scaling

Hatem Barghathi and Adrian Del Maestro

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The second Rényi entropy is readily measured using two-copy protocols and is often used as a proxy for the von Neumann entanglement entropy, where it is assumed to track its asymptotic scaling. B 32, 1850306 (2018)) revealed that in the ground state of some highly constrained spin models, the scaling of the von Neumann and Rényi entropies can differ, varying from power law to logarithmic scaling as a function of the Rényi index. We introduce a symmetry-aware lower bound on the von Neumann entropy built from charge-resolved Rényi entropies that can provide a protocol for diagnosing anomalous entanglement scaling from experimentally accessible data.

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AbstractThe scaling of entanglement with subsystem size encodes key information about phases and criticality, but the von Neumann entropy is costly to access in experiments and simulations, often requiring full state tomography. The second Rényi entropy is readily measured using two-copy protocols and is often used as a proxy for the von Neumann entanglement entropy, where it is assumed to track its asymptotic scaling. Sugino and Korepiny (Int. J. Mod. Phys. B 32, 1850306 (2018)) revealed that in the ground state of some highly constrained spin models, the scaling of the von Neumann and Rényi entropies can differ, varying from power law to logarithmic scaling as a function of the Rényi index. Here, we construct a number-conserving many-body state that demonstrates a Rényi-index-dependent change in the leading entanglement scaling, generalizing previous results to the case of interacting fermions. We introduce a symmetry-aware lower bound on the von Neumann entropy built from charge-resolved Rényi entropies that can provide a protocol for diagnosing anomalous entanglement scaling from experimentally accessible data.Popular summaryEntanglement is a defining feature of quantum matter, but its most informative measure, the von Neumann entanglement entropy, is difficult to obtain in experiments and large-scale simulations. Researchers therefore often use the easier-to-measure second Rényi entropy and assume that it grows with system size in the same way. We show that this assumption can fail even for a simple particle-number-conserving quantum state: rare particle-number sectors can hide substantial entanglement, so the second Rényi entropy grows only logarithmically while the von Neumann entropy grows much faster. We also introduce a symmetry-aware lower bound that can be constructed from experimentally accessible measurements and used to reveal when the second Rényi entropy is underestimating the true entanglement scaling.► BibTeX data@article{Barghathi2026detectionofrenyi, doi = {10.22331/q-2026-08-07-2184}, url = {https://doi.org/10.22331/q-2026-08-07-2184}, title = {Detection of a {R}{\'{e}}nyi {I}ndex {D}ependent {T}ransition in {E}ntanglement {E}ntropy {S}caling}, author = {Barghathi, Hatem and Del Maestro, Adrian}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2184}, month = aug, year = {2026} }► References [1] Khagendra Adhikariand K. S. D. Beach ``Slow dynamics of the Fredkin spin chain'' Phys. Rev. B 104, 115149 (2021). https://doi.org/10.1103/PhysRevB.104.115149 [2] Anurag Anshu, Itai Arad, and David Gosset, ``An area law for 2d frustration-free spin systems'' 12–18 (2022). https://doi.org/10.1145/3519935.3519962 [3] Mark J. Arildsen, Valentin Crépel, Nicolas Regnault, and Benoit Estienne, ``Symmetry-resolved entanglement entropy in a non-Abelian fractional quantum Hall state'' Phys. Rev. B 113, 075108 (2026). https://doi.org/10.1103/h336-ysly [4] Hatem Barghathi, Emanuel Casiano-Diaz, and Adrian Del Maestro, ``Operationally accessible entanglement of one-dimensional spinless fermions'' Phys. Rev. A 100, 022324 (2019). https://doi.org/10.1103/physreva.100.022324 [5] Hatem Barghathiand Adrian Del Maestro ``Github Repository'' https://github.com/DelMaestroGroup/papers-code-EntanglementScalingTransition (2025). https://doi.org/10.5281/zenodo.18118762 https://zenodo.org/records/18118762 [6] Hatem Barghathi, C. M. Herdman, and Adrian Del Maestro, ``Rényi Generalization of the Accessible Entanglement Entropy'' Phys. Rev. Lett. 121, 150501 (2018). https://doi.org/10.1103/PhysRevLett.121.150501 [7] Eugenio Bianchi, Pietro Dona, and Rishabh Kumar, ``Non-Abelian symmetry-resolved entanglement entropy'' SciPost Physics 17, 127 (2024). https://doi.org/10.21468/scipostphys.17.5.127 https://scipost.org/10.21468/SciPostPhys.17.5.127 [8] G. K. Brennenand A. Miyake ``Measurement-Based Quantum Computer in the Gapped Ground State of a Two-Body Hamiltonian'' Phys. Rev. Lett. 101, 010502 (2008). https://doi.org/10.1103/PhysRevLett.101.010502 [9] H. J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, and M. Van den Nest, ``Measurement-based quantum computation'' Nature Physics 5, 19–26 (2009). https://doi.org/10.1038/nphys1157 [10] Tiff Brydges, Andreas Elben, Petar Jurcevic, Benoît Vermersch, Christine Maier, Ben P. Lanyon, Peter Zoller, Rainer Blatt, and Christian F. Roos, ``Probing Rényi entanglement entropy via randomized measurements'' Science 364, 260 (2019). https://doi.org/10.1126/science.aau4963 [11] Pasquale Calabreseand John Cardy ``Entanglement entropy and quantum field theory'' J. Stat. Mech.: Theor. Exp. 2004, 06002 (2004). https://doi.org/10.1088/1742-5468/2004/06/p06002 https://iopscience.iop.org/article/10.1088/1742-5468/2004/06/P06002 [12] Pasquale Calabrese, Jérôme Dubail, and Sara Murciano, ``Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models'' J.

High Energy Phys. 10, 067 (2021). https://doi.org/10.1007/jhep10(2021)067 [13] Emanuel Casiano-Diaz, C. M. Herdman, and Adrian Del Maestro, ``A path integral ground state Monte Carlo algorithm for entanglement of lattice bosons'' SciPost Physics 14, 054 (2023). https://doi.org/10.21468/scipostphys.14.3.054 arXiv:2207.11301 [14] Olalla A. Castro-Alvaredoand Lucía Santamaría-Sanz ``Symmetry-resolved measures in quantum field theory: A short review'' Modern Physics Letters B 39, 2430002 (2025). https://doi.org/10.1142/S0217984924300023 [15] Debarghya Chakrabortyand Nikolaos Angelinos ``Entanglement entropy in ground states of long-range fermionic systems'' Phys. Rev. A 110, 042408 (2024). https://doi.org/10.1103/physreva.110.042408 [16] A. J. Daley, H. Pichler, J. Schachenmayer, and P. Zoller, ``Measuring Entanglement Growth in Quench Dynamics of Bosons in an Optical Lattice'' Phys. Rev. Lett. 109, 020505 (2012). https://doi.org/10.1103/PhysRevLett.109.020505 [17] L. Dell'Anna, O. Salberger, L. Barbiero, A. Trombettoni, and V. E. Korepin, ``Violation of cluster decomposition and absence of light cones in local integer and half-integer spin chains'' Phys. Rev. B 94, 155140 (2016). https://doi.org/10.1103/PhysRevB.94.155140 [18] Xiaolong Dengand Luis Santos ``Entanglement spectrum of one-dimensional extended Bose-Hubbard models'' Phys. Rev. B 84, 085138 (2011). https://doi.org/10.1103/PhysRevB.84.085138 [19] Jonathan D’Emidioand Anders W. Sandvik ``Entanglement Entropy and Deconfined Criticality: Emergent SO(5) Symmetry and Proper Lattice Bipartition'' Phys. Rev. Lett. 133, 166702 (2024). https://doi.org/10.1103/physrevlett.133.166702 [20] J. Eisert, M. Cramer, and M. B. Plenio, ``Colloquium: Area laws for the entanglement entropy'' Rev. Mod. Phys. 82, 277–306 (2010). https://doi.org/10.1103/RevModPhys.82.277 [21] A. Elben, B. Vermersch, M. Dalmonte, J. I. Cirac, and P. Zoller, ``Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models'' Phys. Rev. Lett. 120, 050406 (2018). https://doi.org/10.1103/physrevlett.120.050406 [22] A. Elben, B. Vermersch, C. F. Roos, and P. Zoller, ``Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many-body quantum states'' Phys. Rev. A 99, 052323 (2019). https://doi.org/10.1103/physreva.99.052323 [23] D. V. Else, I. Schwarz, S. D. Bartlett, and A. C. Doherty, ``Symmetry-Protected Phases for Measurement-Based Quantum Computation'' Phys. Rev. Lett. 108, 240505 (2012). https://doi.org/10.1103/PhysRevLett.108.240505 [24] T. Giamarchi ``Quantum Physics in One Dimension'' Clarendon Press (2004). [25] Dimitri Gioevand Israel Klich ``Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture'' Phys. Rev. Lett. 96, 100503 (2006). https://doi.org/10.1103/PhysRevLett.96.100503 [26] Moshe Goldsteinand Eran Sela ``Symmetry-Resolved Entanglement in Many-Body Systems'' Phys. Rev. Lett. 120, 200602 (2018). https://doi.org/10.1103/PhysRevLett.120.200602 [27] D. Gross, S. T. Flammia, and J. Eisert, ``Most Quantum States Are Too Entangled To Be Useful As Computational Resources'' Phys. Rev. Lett. 102, 190501 (2009). https://doi.org/10.1103/PhysRevLett.102.190501 [28] Tarun Grover ``Entanglement of Interacting Fermions in Quantum Monte Carlo Calculations'' Phys. Rev. Lett. 111, 130402 (2013). https://doi.org/10.1103/physrevlett.111.130402 [29] R. V. L. Hartley ``Transmission of information'' The Bell System Technical Journal 7, 535–563 (1928). https://doi.org/10.1002/j.1538-7305.1928.tb01236.x [30] M B Hastings ``An area law for one-dimensional quantum systems'' Journal of Statistical Mechanics: Theory and Experiment 2007, P08024 (2007). https://doi.org/10.1088/1742-5468/2007/08/P08024 [31] Matthew B. Hastings, Iván González, Ann B. Kallin, and Roger G. Melko, ``Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations'' Phys. Rev. Lett. 104, 157201 (2010). https://doi.org/10.1103/physrevlett.104.157201 [32] Johannes Helmesand Stefan Wessel ``Entanglement entropy scaling in the bilayer Heisenberg spin system'' Phys. Rev. B 89, 245120 (2014). https://doi.org/10.1103/PhysRevB.89.245120 [33] C. M. Herdman, P.-N. Roy, R. G. Melko, and A. Del Maestro, ``Entanglement area law in superfluid 4He'' Nature Phys. 13, 556 (2017). https://doi.org/10.1038/nphys4075 https://www.nature.com/articles/nphys4075 [34] C. M. Herdman, Stephen Inglis, P. N. Roy, R. G. Melko, and A. Del Maestro, ``Path-integral Monte Carlo method for Rényi entanglement entropies'' Phys. Rev. E 90, 013308 (2014). https://doi.org/10.1103/physreve.90.013308 [35] Christoph Holzhey, Finn Larsen, and Frank Wilczek, ``Geometric and renormalized entropy in conformal field theory'' Nuclear Physics B 424, 443–467 (1994). https://doi.org/10.1016/0550-3213(94)90402-2 https://www.sciencedirect.com/science/article/pii/0550321394904022 [36] Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, and Karol Horodecki, ``Quantum entanglement'' Rev. Mod. Phys. 81, 865–942 (2009). https://doi.org/10.1103/RevModPhys.81.865 [37] Dávid X. Horváthand Pasquale Calabrese ``Symmetry resolved entanglement in integrable field theories via form factor bootstrap'' J.

High Energy Phys. 2020, 131 (2020). https://doi.org/10.1007/JHEP11(2020)131 [38] David X. Horvath, Pasquale Calabrese, and Olalla A. Castro-Alvaredo, ``Branch Point Twist Field Form Factors in the sine-Gordon Model II: Composite Twist Fields and Symmetry Resolved Entanglement'' SciPost Phys. 12, 088 (2022). https://doi.org/10.21468/SciPostPhys.12.3.088 [39] Liza Huijseand Brian Swingle ``Area law violations in a supersymmetric model'' Phys. Rev. B 87, 035108 (2013). https://doi.org/10.1103/PhysRevB.87.035108 [40] Sandy Irani ``Ground state entanglement in one-dimensional translationally invariant quantum systems'' Journal of Mathematical Physics 51, 022101 (2010). https://doi.org/10.1063/1.3254321 [41] Sergei V. Isakov, Matthew B. Hastings, and Roger G. Melko, ``Topological entanglement entropy of a Bose–Hubbard spin liquid'' Nature Phys. 7, 772 (2011). https://doi.org/10.1038/nphys2036 https://www.nature.com/articles/nphys2036 [42] Rajibul Islam, Ruichao Ma, Philipp M. Preiss, M. Eric Tai, Alexander Lukin, Matthew Rispoli, and Markus Greiner, ``Measuring entanglement entropy in a quantum many-body system'' Nature 528, 77 (2015). https://doi.org/10.1038/nature15750 https://www.nature.com/articles/nature15750 [43] J. L. W. V. Jensen ``Sur les fonctions convexes et les inégalités entre les valeurs moyennes'' Acta Mathematica 30, 175–193 (1906). https://doi.org/10.1007/bf02418571 [44] Adam M. Kaufman, M. Eric Tai, Alexander Lukin, Matthew Rispoli, Robert Schittko, Philipp M. Preiss, and Markus Greiner, ``Quantum thermalization through entanglement in an isolated many-body system'' Science 353, 794 (2016). https://doi.org/10.1126/science.aaf6725 [45] Maximilian Kiefer-Emmanouilidis, Razmik Unanyan, Jesko Sirker, and Michael Fleischhauer, ``Bounds on the entanglement entropy by the number entropy in non-interacting fermionic systems'' SciPost Phys. 8, 083 (2020). https://doi.org/10.21468/SciPostPhys.8.6.083 [46] Maximilian Kiefer-Emmanouilidis, Razmik Unanyan, Michael Fleischhauer, and Jesko Sirker, ``Evidence for Unbounded Growth of the Number Entropy in Many-Body Localized Phases'' Phys. Rev. Lett. 124, 243601 (2020). https://doi.org/10.1103/PhysRevLett.124.243601 [47] I. Klichand L. S. Levitov ``Scaling of entanglement entropy and superselection rules'' (2008). arXiv:0812.0006 [48] V. E. Korepin ``Universality of Entropy Scaling in One Dimensional Gapless Models'' Phys. Rev. Lett. 92, 096402 (2004). https://doi.org/10.1103/PhysRevLett.92.096402 [49] Nicolas Laflorencie ``Quantum entanglement in condensed matter systems'' Physics Reports 646, 1–59 (2016) Quantum entanglement in condensed matter system. https://doi.org/10.1016/j.physrep.2016.06.008 https://www.sciencedirect.com/science/article/pii/S0370157316301582 [50] Hajo Leschke, Alexander V. Sobolev, and Wolfgang Spitzer, ``Scaling of Rényi Entanglement Entropies of the Free Fermi-Gas Ground State: A Rigorous Proof'' Phys. Rev. Lett. 112, 160403 (2014). https://doi.org/10.1103/PhysRevLett.112.160403 [51] Alexander Lukin, Matthew Rispoli, Robert Schittko, M. Eric Tai, Adam M. Kaufman, Soonwon Choi, Vedika Khemani, Julian Léonard, and Markus Greiner, ``Probing entanglement in a many-body–localized system'' Science 364, 256 (2019). https://doi.org/10.1126/science.aau0818 [52] Han Ma, A. T. Schmitz, S. A. Parameswaran, Michael Hermele, and Rahul M. Nandkishore, ``Topological entanglement entropy of fracton stabilizer codes'' Phys. Rev. B 97, 125101 (2018). https://doi.org/10.1103/physrevb.97.125101 [53] Jeremy McMinisand Norm M. Tubman ``Renyi entropy of the interacting Fermi liquid'' Phys. Rev. B 87, 081108 (2013). https://doi.org/10.1103/physrevb.87.081108 [54] R. G. Melko, C. M. Herdman, D. Iouchtchenko, P.-N. Roy, and A. Del Maestro, ``Entangling qubit registers via many-body states of ultracold atoms'' Phys. Rev. A 93, 042336 (2016). https://doi.org/10.1103/physreva.93.042336 [55] Varun Menon, Andi Gu, and Ramis Movassagh, ``Symmetries, correlation functions, and entanglement of general quantum Motzkin spin-chains'' (2024). arXiv:2408.16070 [56] Kyle Monkmanand Jesko Sirker ``Operational entanglement of symmetry-protected topological edge states'' Phys. Rev. Res. 2, 043191 (2020). https://doi.org/10.1103/PhysRevResearch.2.043191 [57] Kyle Monkmanand Jesko Sirker ``Symmetry-resolved entanglement: general considerations, calculation from correlation functions, and bounds for symmetry-protected topological phases'' Journal of Physics A: Mathematical and Theoretical 56, 495001 (2023). https://doi.org/10.1088/1751-8121/ad086d [58] Kyle Monkmanand Jesko Sirker ``Symmetry-resolved entanglement of ${C}_{2}$-symmetric topological insulators'' Phys. Rev. B 107, 125108 (2023). https://doi.org/10.1103/PhysRevB.107.125108 [59] Ramis Movassaghand Peter W. Shor ``Supercritical entanglement in local systems: Counterexample to the area law for quantum matter'' Proceedings of the National Academy of Sciences 113, 13278–13282 (2016). https://doi.org/10.1073/pnas.1605716113 [60] Kaustav Mukherjee, Hatem Barghathi, Adrian Del Maestro, and Rick Mukherjee, ``Quantum simulation of Motzkin spin chain with Rydberg atoms'' (2026). arXiv:2603.23422 [61] Sara Murciano, Riccarda Bonsignori, and Pasquale Calabrese, ``Symmetry decomposition of negativity of massless free fermions'' SciPost Phys. 10, 111 (2021). https://doi.org/10.21468/SciPostPhys.10.5.111 [62] M. Van den Nest, W. Dür, A. Miyake, and H. J. Briegel, ``Universal Resources for Measurement-Based Quantum Computation'' Phys. Rev. Lett. 97, 150504 (2006). https://doi.org/10.1103/PhysRevLett.97.150504 [63] M. Ghasemi Nezhadhaghighiand M. A. Rajabpour ``Quantum entanglement entropy and classical mutual information in long-range harmonic oscillators'' Phys. Rev. B 88, 045426 (2013). https://doi.org/10.1103/physrevb.88.045426 [64] Gilles Parez ``Symmetry-resolved Rényi fidelities and quantum phase transitions'' Phys. Rev. B 106, 235101 (2022). https://doi.org/10.1103/PhysRevB.106.235101 [65] Hannes Pichler, Guanyu Zhu, Alireza Seif, Peter Zoller, and Mohammad Hafezi, ``Measurement Protocol for the Entanglement Spectrum of Cold Atoms'' Phys. Rev. X 6, 041033 (2016). https://doi.org/10.1103/physrevx.6.041033 [66] Iztok Pižorn, Frank Verstraete, and Robert M. Konik, ``Tree tensor networks and entanglement spectra'' Phys. Rev. B 88, 195102 (2013). https://doi.org/10.1103/PhysRevB.88.195102 [67] F Pollmannand J E Moore ``Entanglement spectra of critical and near-critical systems in one dimension'' New Journal of Physics 12, 025006 (2010). https://doi.org/10.1088/1367-2630/12/2/025006 [68] R. Raussendorfand H. J. Briegel ``A One-Way Quantum Computer'' Phys. Rev. Lett. 86, 5188–5191 (2001). https://doi.org/10.1103/PhysRevLett.86.5188 [69] R. Raussendorfand J. Harrington ``Fault-Tolerant Quantum Computation with High Threshold in Two Dimensions'' Phys. Rev. Lett. 98, 190504 (2007). https://doi.org/10.1103/PhysRevLett.98.190504 [70] Christoph Simon ``Natural entanglement in Bose-Einstein condensates'' Phys. Rev. A 66, 052323 (2002). https://doi.org/10.1103/PhysRevA.66.052323 [71] Mark Srednicki ``Entropy and area'' Phys. Rev. Lett. 71, 666–669 (1993). https://doi.org/10.1103/PhysRevLett.71.666 [72] Fumihiko Suginoand Vladimir Korepin ``Rényi entropy of highly entangled spin chains'' International Journal of Modern Physics B 32, 1850306 (2018). https://doi.org/10.1142/S021797921850306X [73] Brian Swingle ``Entanglement renormalization and holography'' Phys. Rev. D 86, 065007 (2012). https://doi.org/10.1103/physrevd.86.065007 [74] G. Vidal ``Efficient Classical Simulation of Slightly Entangled Quantum Computations'' Phys. Rev. Lett. 91, 147902 (2003). https://doi.org/10.1103/PhysRevLett.91.147902 [75] G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, ``Entanglement in Quantum Critical Phenomena'' Phys. Rev. Lett. 90, 227902 (2003). https://doi.org/10.1103/PhysRevLett.90.227902 [76] G Vitagliano, A Riera, and J I Latorre, ``Volume-law scaling for the entanglement entropy in spin-1/2 chains'' New Journal of Physics 12, 113049 (2010). https://doi.org/10.1088/1367-2630/12/11/113049 [77] Jianyu Wang, Zenan Liu, Zheng Yan, and Congjun Wu, ``Singularity and universality from von Neumann to Rényi entanglement entropy and disorder operator in Motzkin chains'' Phys. Rev. B 112, 075128 (2025). https://doi.org/10.1103/wffk-7ycs [78] Lei Wangand Matthias Troyer ``Renyi Entanglement Entropy of Interacting Fermions Calculated Using the Continuous-Time Quantum Monte Carlo Method'' Phys. Rev. Lett. 113, 110401 (2014). https://doi.org/10.1103/physrevlett.113.110401 [79] Julia Wildeboer, Alexander Seidel, and Roger G. Melko, ``Entanglement entropy and topological order in resonating valence-bond quantum spin liquids'' Phys. Rev. B 95, 100402 (2017). https://doi.org/10.1103/physrevb.95.100402 [80] H. M. Wisemanand John A. Vaccaro ``Entanglement of Indistinguishable Particles Shared between Two Parties'' Phys. Rev. Lett. 91, 097902 (2003). https://doi.org/10.1103/PhysRevLett.91.097902 [81] Michael M. Wolf ``Violation of the Entropic Area Law for Fermions'' Phys. Rev. Lett. 96, 010404 (2006). https://doi.org/10.1103/PhysRevLett.96.010404 [82] Jiarui Zhao, Nicolas Laflorencie, and Zi Yang Meng, ``Unconventional Scalings of Quantum Entropies in Long-Range Heisenberg Chains'' Phys. Rev. Lett. 134, 016707 (2025). https://doi.org/10.1103/PhysRevLett.134.016707 [83] Jiarui Zhao, Yan-Cheng Wang, Zheng Yan, Meng Cheng, and Zi Yang Meng, ``Scaling of Entanglement Entropy at Deconfined Quantum Criticality'' Phys. Rev. Lett. 128, 010601 (2022). https://doi.org/10.1103/physrevlett.128.010601Cited by[1] Kaustav Mukherjee, Hatem Barghathi, Adrian Del Maestro, and Rick Mukherjee, "Quantum simulation of Motzkin spin chain with Rydberg atoms", arXiv:2603.23422, (2026). [2] Aleksandrs Sokolovs, "Rényi exponent landscape of multipartite entanglement in free-fermion systems", arXiv:2603.08991, (2026). [3] Ang-Kun Wu, Louis Primeau, Yixin Zhang, Jingtao Zhang, Adrian Del Maestro, and Yang Zhang, "Compact Spin-Charge Separated Neural Quantum States for Valence-Bond States", arXiv:2606.17045, (2026). The above citations are from SAO/NASA ADS (last updated successfully 2026-08-07 12:49:49). The list may be incomplete as not all publishers provide suitable and complete citation data.Could not fetch Crossref cited-by data during last attempt 2026-08-07 12:49:48: Could not fetch cited-by data for 10.22331/q-2026-08-07-2184 from Crossref. This is normal if the DOI was registered recently.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractThe scaling of entanglement with subsystem size encodes key information about phases and criticality, but the von Neumann entropy is costly to access in experiments and simulations, often requiring full state tomography. The second Rényi entropy is readily measured using two-copy protocols and is often used as a proxy for the von Neumann entanglement entropy, where it is assumed to track its asymptotic scaling. Sugino and Korepiny (Int. J. Mod. Phys. B 32, 1850306 (2018)) revealed that in the ground state of some highly constrained spin models, the scaling of the von Neumann and Rényi entropies can differ, varying from power law to logarithmic scaling as a function of the Rényi index. Here, we construct a number-conserving many-body state that demonstrates a Rényi-index-dependent change in the leading entanglement scaling, generalizing previous results to the case of interacting fermions. We introduce a symmetry-aware lower bound on the von Neumann entropy built from charge-resolved Rényi entropies that can provide a protocol for diagnosing anomalous entanglement scaling from experimentally accessible data.Popular summaryEntanglement is a defining feature of quantum matter, but its most informative measure, the von Neumann entanglement entropy, is difficult to obtain in experiments and large-scale simulations. Researchers therefore often use the easier-to-measure second Rényi entropy and assume that it grows with system size in the same way. We show that this assumption can fail even for a simple particle-number-conserving quantum state: rare particle-number sectors can hide substantial entanglement, so the second Rényi entropy grows only logarithmically while the von Neumann entropy grows much faster. We also introduce a symmetry-aware lower bound that can be constructed from experimentally accessible measurements and used to reveal when the second Rényi entropy is underestimating the true entanglement scaling.► BibTeX data@article{Barghathi2026detectionofrenyi, doi = {10.22331/q-2026-08-07-2184}, url = {https://doi.org/10.22331/q-2026-08-07-2184}, title = {Detection of a {R}{\'{e}}nyi {I}ndex {D}ependent {T}ransition in {E}ntanglement {E}ntropy {S}caling}, author = {Barghathi, Hatem and Del Maestro, Adrian}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2184}, month = aug, year = {2026} }► References [1] Khagendra Adhikariand K. S. D. Beach ``Slow dynamics of the Fredkin spin chain'' Phys. Rev. B 104, 115149 (2021). https://doi.org/10.1103/PhysRevB.104.115149 [2] Anurag Anshu, Itai Arad, and David Gosset, ``An area law for 2d frustration-free spin systems'' 12–18 (2022). https://doi.org/10.1145/3519935.3519962 [3] Mark J. Arildsen, Valentin Crépel, Nicolas Regnault, and Benoit Estienne, ``Symmetry-resolved entanglement entropy in a non-Abelian fractional quantum Hall state'' Phys. Rev. B 113, 075108 (2026). https://doi.org/10.1103/h336-ysly [4] Hatem Barghathi, Emanuel Casiano-Diaz, and Adrian Del Maestro, ``Operationally accessible entanglement of one-dimensional spinless fermions'' Phys. Rev. A 100, 022324 (2019). https://doi.org/10.1103/physreva.100.022324 [5] Hatem Barghathiand Adrian Del Maestro ``Github Repository'' https://github.com/DelMaestroGroup/papers-code-EntanglementScalingTransition (2025). https://doi.org/10.5281/zenodo.18118762 https://zenodo.org/records/18118762 [6] Hatem Barghathi, C. M. Herdman, and Adrian Del Maestro, ``Rényi Generalization of the Accessible Entanglement Entropy'' Phys. Rev. Lett. 121, 150501 (2018). https://doi.org/10.1103/PhysRevLett.121.150501 [7] Eugenio Bianchi, Pietro Dona, and Rishabh Kumar, ``Non-Abelian symmetry-resolved entanglement entropy'' SciPost Physics 17, 127 (2024). https://doi.org/10.21468/scipostphys.17.5.127 https://scipost.org/10.21468/SciPostPhys.17.5.127 [8] G. K. Brennenand A. Miyake ``Measurement-Based Quantum Computer in the Gapped Ground State of a Two-Body Hamiltonian'' Phys. Rev. Lett. 101, 010502 (2008). https://doi.org/10.1103/PhysRevLett.101.010502 [9] H. J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, and M. Van den Nest, ``Measurement-based quantum computation'' Nature Physics 5, 19–26 (2009). https://doi.org/10.1038/nphys1157 [10] Tiff Brydges, Andreas Elben, Petar Jurcevic, Benoît Vermersch, Christine Maier, Ben P. Lanyon, Peter Zoller, Rainer Blatt, and Christian F. Roos, ``Probing Rényi entanglement entropy via randomized measurements'' Science 364, 260 (2019). https://doi.org/10.1126/science.aau4963 [11] Pasquale Calabreseand John Cardy ``Entanglement entropy and quantum field theory'' J. Stat. Mech.: Theor. Exp. 2004, 06002 (2004). https://doi.org/10.1088/1742-5468/2004/06/p06002 https://iopscience.iop.org/article/10.1088/1742-5468/2004/06/P06002 [12] Pasquale Calabrese, Jérôme Dubail, and Sara Murciano, ``Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models'' J.

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