Extreme statistics as a probe of the superfluid to Bose-glass Berezinskii-Kosterlitz-Thouless transition

Abstract

Recent studies of delocalization-localization transitions in disordered quantum chains have highlighted the role of rare, chain-breaking events that favor localization, in particular for high-energy eigenstates related to many-body localization. In this context, we revisit the random-field XXZ spin-1/2 chain at zero temperature with ferromagnetic interactions, equivalent to interacting fermions or hard-core bosons in a random potential with attractive interactions. We argue that localization in this model can be characterized by chain-breaking events, which are probed by the extreme values of simple local observables, such as the on-site density or the local magnetization, that are readily accessible in both experiments and numerical simulations. Adopting a bosonic language, we study the disorder-induced Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition from superfluid (SF) to Bose glass (BG), and focus on the strong disorder regime where localization is driven by weak links. Based on high-precision density matrix renormalization group simulations, we numerically show that extreme local densities accurately capture the BKT transition, even for relatively short chains ranging from a few dozen to a hundred sites. We also discuss the SF-BG transition in the weak disorder regime, where finite-size effects pose greater challenges. Overall, our work seeks to establish a solid foundation for using extreme statistics of local observables, such as density, to probe delocalization-localization transitions in disordered quantum chains, both in the ground state and at high energy.

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Cite

BibTeX RIS

BibTeX

@article{colbois2026extreme,
  title = {{Extreme statistics as a probe of the superfluid to Bose-glass Berezinskii-Kosterlitz-Thouless transition}},
  author = {Jeanne Colbois and Natalia Chepiga and Shaffique Adam and Gabriel Lemarié and Nicolas Laflorencie},
  journal = {New Journal of Physics},
  year = {2026},
  month = oct,
  doi = {10.1088/1367-2630/ae9397},
  eprint = {2512.09029},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05412001v1},
  note = {CC BY-NC 4.0},
}

RIS

TY  - JOUR
TI  - Extreme statistics as a probe of the superfluid to Bose-glass Berezinskii-Kosterlitz-Thouless transition
AU  - Jeanne Colbois
AU  - Natalia Chepiga
AU  - Shaffique Adam
AU  - Gabriel Lemarié
AU  - Nicolas Laflorencie
PY  - 2026
DA  - 2026/10/02
JO  - New Journal of Physics
DO  - 10.1088/1367-2630/ae9397
UR  - https://hal.science/hal-05412001v1
AB  - Recent studies of delocalization-localization transitions in disordered quantum chains have highlighted the role of rare, chain-breaking events that favor localization, in particular for high-energy eigenstates related to many-body localization. In this context, we revisit the random-field XXZ spin-1/2 chain at zero temperature with ferromagnetic interactions, equivalent to interacting fermions or hard-core bosons in a random potential with attractive interactions. We argue that localization in this model can be characterized by chain-breaking events, which are probed by the extreme values of simple local observables, such as the on-site density or the local magnetization, that are readily accessible in both experiments and numerical simulations. Adopting a bosonic language, we study the disorder-induced Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition from superfluid (SF) to Bose glass (BG), and focus on the strong disorder regime where localization is driven by weak links. Based on high-precision density matrix renormalization group simulations, we numerically show that extreme local densities accurately capture the BKT transition, even for relatively short chains ranging from a few dozen to a hundred sites. We also discuss the SF-BG transition in the weak disorder regime, where finite-size effects pose greater challenges. Overall, our work seeks to establish a solid foundation for using extreme statistics of local observables, such as density, to probe delocalization-localization transitions in disordered quantum chains, both in the ground state and at high energy.
SN  - 1367-2630
ER  -

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