- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Entanglement halos

Nadir Samos Sáenz de Buruaga1,2,*, Silvia N. Santalla3, Germán Sierra4,5, and Javier Rodríguez-Laguna6

  • *Contact author: nadir.samos@uam.es
PDF

Phys. Rev. Research 8, 013114 – Published 30 January, 2026

DOI: https://doi.org/10.1103/fddq-8lzl

Abstract

We introduce the concept of entanglement halos, a set of strongly entangled distant sites within the ground state of a quantum many-body system. Such halos emerge in starlike systems with exponentially decaying couplings, as we show using both free fermions and the spin-1/2 antiferromagnetic Heisenberg model. Depending on the central connectivity, entanglement halos may exhibit trivial and nontrivial symmetry-protected topological features. Our findings highlight how geometry and connectivity can generate complex entanglement structures with rich physical content, which can be experimentally accessible via state-of-the-art technologies.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (52)

  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2010).
  2. B. Zeng, X. Chen, D. L. Zhou, and X. G. Wen, Quantum Information Meets Quantum Matter (Springer, Berlin, 2019).
  3. D. Harlow, Jerusalem lectures on black holes and quantum information, Rev. Mod. Phys. 88, 015002 (2016).
  4. G. Adesso, T. R. Bromley, and M. Cianciaruso, Measures and applications of quantum correlations, J. Phys. A: Math. Theor. 49, 473001 (2016).
  5. F. Arute, et al., Quantum supremacy using a programmable superconducting processor, Nature (London) 574, 505 (2019).
  6. X.-G. Wen, Topological order: From long-range entangled quantum matter to a unified origin of light and electrons, Int. Schol. Res. Not. 2013, 198710 (2013).
  7. X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, Symmetry protected topological orders and the group cohomology of their symmetry group, Phys. Rev. B 87, 155114 (2013).
  8. N. Schuch, D. Pérez-García, and I. Cirac, Classifying quantum phases using matrix product states and projected entangled pair states, Phys. Rev. B 84, 165139 (2011).
  9. M. Van Raamsdonk, Building up space–time with quantum entanglement, Int. J. Mod. Phys. D 19, 2429 (2010).
  10. A. R. Brown, H. Gharibyan, S. Leichenauer, H. W. Lin, S. Nezami, G. Salton, L. Susskind, B. Swingle, and M. Walter, Quantum gravity in the lab. I. Teleportation by size and traversable wormholes, PRX Quantum 4, 010320 (2023).
  11. L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80, 517 (2008).
  12. N. Laflorencie, Quantum entanglement in condensed matter systems, Phys. Rep. 646, 1 (2016).
  13. J. I. Cirac, D. Pérez-García, N. Schuch, and F. Verstraete, Matrix product states and projected entangled pair states: Concepts, symmetries, and theorems, Rev. Mod. Phys. 93, 045003 (2021).
  14. G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Entanglement in quantum critical phenomena, Phys. Rev. Lett. 90, 227902 (2003).
  15. P. Calabrese and J. L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. (2004) P06002.
  16. G. Vitagliano, A. Riera, and J. I. Latorre, Volume-law scaling for the entanglement entropy in spin-1/2 chains, New J. Phys. 12, 113049 (2010).
  17. G. Ramírez, J. Rodríguez-Laguna, and G. Sierra, From conformal to volume-law for the entanglement entropy in exponentially deformed critical spin 1/2 chains, J. Stat. Mech. (2014) P10004.
  18. G. Ramírez, J. Rodríguez-Laguna, and G. Sierra, Entanglement over the rainbow, J. Stat. Mech. (2015) P06002.
  19. C. Dasgupta and S. K. Ma, Low temperature properties of the random Heisenberg antiferromagnetic chain, Phys. Rev. B 22, 1305 (1980).
  20. F. Iglói and C. Monthus, Strong disorder RG approach—A short review of recent developments, Eur. Phys. J. B 91, 290 (2018).
  21. B. T. Draine, Interstellar dust grains, Annu. Rev. Astron. Astrophys. 41, 241 (2003).
  22. A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, and C. I. Westbrook, Observation of atom pairs in spontaneous four-wave mixing of two colliding Bose-Einstein condensates, Phys. Rev. Lett. 99, 150405 (2007).
  23. D. K. Shin, et al., Bell correlations between spatially separated pairs of atoms, Nat. Commun. 10, 4447 (2019).
  24. D. K. Shin, J. A. Ross, B. M. Henson, S. S. Hodgman, and A. G. Truscott, Entanglement-based 3D magnetic gradiometry with an ultracold atomic scattering halo, New J. Phys. 22, 013002 (2020).
  25. L. Savary and L. Balents, Quantum spin liquids: A review, Rep. Prog. Phys. 80, 016502 (2017).
  26. L. Lyu, D. Chandorkar, S. Kapoor, S. Takei, E. S. Sørensen, and W. Witczak-Krempa, Multiparty entanglement loops in quantum spin liquids, arXiv:2505.18124.
  27. P. Calabrese, M. Mintchev, and E. Vicari, Entanglement entropy of quantum wire junctions, J. Phys. A: Math. Theor. 45, 105206 (2012).
  28. N. Crampé and A. Trombettoni, Quantum spins on star graphs and the Kondo model, Nucl. Phys. B 871, 526 (2013).
  29. R. Juhász, J. M. Oberreuter, and Z. Zimborás, Entanglement entropy of disordered quantum wire junctions, J. Stat. Mech. (2018) 123106.
  30. H. Santos, J. E. Alvarellos, and J. Rodríguez-Laguna, Entanglement detachment in fermionic systems, Eur. Phys. J. D 72, 203 (2018).
  31. Z. Zhang, Entanglement blossom in a simplex matryoshka, Ann. Phys. 457, 169395 (2023).
  32. Observe that the Jordan-Wigner transformation does not map this model to an XX spin system.
  33. J. Rodríguez-Laguna, S. N. Santalla, G. Ramirez, and G. Sierra, Entanglement in correlated random spin chains, RNA folding and kinetic roughening, New J. Phys. 18, 073025 (2016).
  34. G. Ramírez, J. Rodríguez-Laguna, and G. Sierra, Entanglement in low-energy states of the random-hopping model, J. Stat. Mech. (2014) P07003.
  35. N. Samos Sáenz de Buruaga, S. N. Santalla, J. Rodríguez-Laguna, and G. Sierra, Symmetry protected phases in inhomogeneous spin chains, J. Stat. Mech. (2019) 093102.
  36. A. Altland and M. R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55, 1142 (1997).
  37. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene, Phys. Rev. Lett. 42, 1698 (1979).
  38. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Rigorous results on valence-bond ground states in antiferromagnets, Phys. Rev. Lett. 59, 799 (1987).
  39. R. Islam, R. Ma, P. M. Preiss, M. E. Tai, A. Lukin, M. Rispoli, and M. Greiner, Measuring entanglement entropy in a quantum many-body system, Nature (London) 528, 77 (2015).
  40. Z. K. Lin, Y. Zhou, B. Jiang, B. Q. Wu, L. M. Chen, X. Y. Liu, L. W. Wang, P. Ye, and J. H. Jiang, Measuring entanglement entropy and its topological signature for phononic systems, Nat. Commun. 15, 1601 (2024).
  41. I. Klich, Lower entropy bounds and particle number fluctuations in a Fermi sea, J. Phys. A: Math. Gen. 39, L85 (2006).
  42. J. Rodríguez-Laguna, L. M. Robledo, and J. Dukelsky, Efficient computation of matrix elements of generic Slater determinants, Phys. Rev. A 101, 012105 (2020).
  43. M. den Nijs and K. Rommelse, Preroughening transitions in crystal surfaces and valence-bond phases in quantum spin chains, Phys. Rev. B 40, 4709 (1989).
  44. O. Boada, A. Celi, J. I. Latorre, and M. Lewenstein, Quantum simulation of an extra dimension, Phys. Rev. Lett. 108, 133001 (2012).
  45. O. Boada, A. Celi, J. Rodríguez-Laguna, J. I. Latorre, and M. Lewenstein, Quantum simulation of non-trivial topology, New J. Phys. 17, 045007 (2015).
  46. T. Ozawa and H. M. Price, Topological quantum matter in synthetic dimensions, Nat. Rev. Phys. 1, 349 (2019).
  47. A. J. Kollár, M. Fitzpatrick, and A. A. Houck, Hyperbolic lattices in circuit quantum electrodynamics, Nature (London) 571, 45 (2019).
  48. J. Rodríguez-Laguna, J. Dubaîl, G. Ramírez, P. Calabrese, and G. Sierra, More on the rainbow chain: Entanglement, space-time geometry and thermal states, J. Phys. A: Math. Theor. 50, 164001 (2017).
  49. N. Samos Sáenz de Buruaga, S. N. Santalla, J. Rodríguez-Laguna, and G. Sierra, Entanglement in non-critical inhomogeneous quantum chains, Phys. Rev. B 104, 195147 (2021).
  50. S. R. White, Equivalence of the antiferromagnetic Heisenberg ladder to a single S = 1 chain, Phys. Rev. B 53, 52 (1996).
  51. P. Sompet, et al., Realizing the symmetry-protected Haldane phase in Fermi–Hubbard ladders, Nature (London) 606, 484 (2022).
  52. The factor 2 in the denominator could be surprising since it appears in the SDRG of a Heisenberg spin-1/2 chain and not in the XX chain or a free fermion chain by means of a Jordan-Wigner transformation. Indeed, notice that we recover J(2)=J12/t by setting nB=2 and taking into account that the Hamiltonian equation  (A1) does not describe in this case a closed system.

Outline

Information

Phys. Rev. Research 8, 013114– Published 30 January, 2026
  • Received 4 August 2025
  • Accepted 31 December 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation