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  • Letter
  • Open Access

Phase transitions in full counting statistics of free fermions and directed polymers

James S. Pallister, Samuel H. Pickering, and Dimitri M. Gangardt

Alexander G. Abanov

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Phys. Rev. Research 7, L022008 – Published 8 April, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022008

Abstract

We consider directed polymers in 1+1 spatial dimension under action of an external repulsive potential along a line. Using the exact mapping onto imaginary time evolution of free fermions we find that for sufficiently strong potential the system of polymers undergoes a continuous configurational phase transition. The transition corresponds to merging empty regions in the dominant limit shape.

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References (38)

  1. R. Kenyon, Lectures on dimers, arXiv:0910.3129.
  2. J.-M. Stéphan, Extreme boundary conditions and random tilings, SciPost Phys. Lect. Notes 2021, 26 (2021).
  3. D. Z. Rocklin, S. Tan, and P. M. Goldbart, Directed-polymer systems explored via their quantum analogs: Topological constraints and their consequences, Phys. Rev. B 86, 165421 (2012).
  4. D. Z. Rocklin and P. M. Goldbart, Directed-polymer systems explored via their quantum analogs: General polymer interactions and their consequences, Phys. Rev. B 88, 165417 (2013).
  5. V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, UK, 1993).
  6. A. G. Abanov and F. Franchini, Emptiness formation probability for the anisotropic XY spin chain in a magnetic field, Phys. Lett. A 316, 342 (2003).
  7. F. Franchini and A. G. Abanov, Asymptotics of Toeplitz determinants and the emptiness formation probability for the XY spin chain, J. Phys. A 38, 5069 (2005).
  8. A. G. Abanov, Hydrodynamics of correlated systems, in Applications of Random Matrices in Physics, edited by É. Brézin, V. Kazakov, D. Serban, P. Wiegmann, and A. Zabrodin (Springer Netherlands, Dordrecht, 2006), pp. 139–161.
  9. J.-M. Stéphan, Emptiness formation probability, Toeplitz determinants, and conformal field theory, J. Stat. Mech. (2014) P05010.
  10. H.-C. Yeh and A. Kamenev, Emptiness formation probability in one-dimensional Bose liquids, Phys. Rev. A 101, 023623 (2020).
  11. H.-C. Yeh, D. M. Gangardt, and A. Kamenev, Emptiness formation in polytropic quantum liquids, J. Phys. A 55, 064002 (2022).
  12. P.-G. de Gennes, Soluble model for fibrous structures with steric constraints, J. Chem. Phys. 48, 2257 (1968).
  13. L. S. Levitov and G. B. Lesovik, Charge-transport statistics in quantum conductors, JETP Lett. 55, 555 (1992).
  14. Y. Nazarov, Quantum Noise in Mesoscopic Physics (Springer, New York, 2003).
  15. A. Polkovnikov, E. Altman, and E. Demler, Interference between independent fluctuating condensates, Proc. Natl. Acad. Sci. USA 103, 6125 (2006).
  16. V. Gritsev, E. Altman, E. Demler, and A. Polkovnikov, Full quantum distribution of contrast in interference experiments between interacting one-dimensional Bose liquids, Nat. Phys. 2, 705 (2006).
  17. M. Arzamasovs and D. M. Gangardt, Full counting statistics and large deviations in a thermal 1D Bose gas, Phys. Rev. Lett. 122, 120401 (2019).
  18. V. Eisler, Z. Rácz, and F. van Wijland, Magnetization distribution in the transverse Ising chain with energy flux, Phys. Rev. E 67, 056129 (2003).
  19. A. Lamacraft and P. Fendley, Order parameter statistics in the critical quantum Ising chain, Phys. Rev. Lett. 100, 165706 (2008).
  20. D. A. Ivanov and A. G. Abanov, Characterizing correlations with full counting statistics: Classical Ising and quantum XY spin chains, Phys. Rev. E 87, 022114 (2013).
  21. I. Klich and L. Levitov, Quantum noise as an entanglement meter, Phys. Rev. Lett. 102, 100502 (2009).
  22. P. Calabrese, M. Mintchev, and E. Vicari, Entanglement entropy of one-dimensional gases, Phys. Rev. Lett. 107, 020601 (2011).
  23. E. Vicari, Entanglement and particle correlations of fermi gases in harmonic traps, Phys. Rev. A 85, 062104 (2012).
  24. P. Calabrese, P. Le Doussal, and S. N. Majumdar, Random matrices and entanglement entropy of trapped Fermi gases, Phys. Rev. A 91, 012303 (2015).
  25. S. J. Garratt, Z. Weinstein, and E. Altman, Measurements conspire nonlocally to restructure critical quantum states, Phys. Rev. X 13, 021026 (2023).
  26. D. A. Ivanov, A. G. Abanov, and V. V. Cheianov, Counting free fermions on a line: A Fisher–Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit, J. Phys. A 46, 085003 (2013).
  27. M. E. Fisher, Walks, walls, wetting, and melting, J. Stat. Phys. 34, 667 (1984).
  28. V. A. Kazakov and A. A. Migdal, Recent progress in the theory of noncritical strings, Nucl. Phys. B 311, 171 (1988).
  29. S. N. Majumdar, C. Nadal, A. Scardicchio, and P. Vivo, Index distribution of Gaussian random matrices, Phys. Rev. Lett. 103, 220603 (2009).
  30. R. Marino, S. N. Majumdar, G. Schehr, and P. Vivo, Index distribution of Cauchy random matrices, J. Phys. A 47, 055001 (2014).
  31. I. Klich, An elementary derivation of Levitov's formula, Quantum Noise in Mesoscopic Physics, edited by Yu. V. Nazarov (Springer Netherlands, Dordrecht, 2003), pp. 397–402.
  32. P. Deift, A. Its, and I. Krasovsky, Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities, Ann. Math. 174, 1243 (2011).
  33. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L022008 for details of calculations.
  34. F. D. Cunden, P. Facchi, M. Ligabò, and P. Vivo, Third-order phase transition: Random matrices and screened Coulomb gas with hard walls, J. Stat. Phys. 175, 1262 (2019).
  35. R. Marino, S. N. Majumdar, G. Schehr, and P. Vivo, Phase transitions and edge scaling of number variance in gaussian random matrices, Phys. Rev. Lett. 112, 254101 (2014).
  36. R. Marino, S. N. Majumdar, G. Schehr, and P. Vivo, Number statistics for β-ensembles of random matrices: Applications to trapped fermions at zero temperature, Phys. Rev. E 94, 032115 (2016).
  37. N. Smith, P. Le Doussal, S. Majumdar, and G. Schehr, Full counting statistics for interacting trapped fermions, SciPost Phys. 11, 110 (2021).
  38. S. Bocini and J.-M. Stéphan, Non-probabilistic fermionic limit shapes, J. Stat. Mech. (2021) 013204.

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Phys. Rev. Research 7, L022008– Published 8 April, 2025
  • Received 30 May 2024
  • Accepted 11 February 2025
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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.

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