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Universal fluctuations of two localized interacting particles in one dimension

Sen Mu1,2,*, Gabriel Lemarié1,3,4,5,†, and Jiangbin Gong1,3,4,‡

  • *Contact author: senmu@u.nus.edu
  • †Contact author: lemarie@irsamc.ups-tlse.fr
  • ‡Contact author: phygj@nus.edu.sg
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Phys. Rev. B 112, 014201 – Published 2 July, 2025

DOI: https://doi.org/10.1103/7d45-yrwq

Abstract

We investigate the universal fluctuations of localized wave functions in the Fock space of two interacting particles in one-dimensional disordered systems, focusing on the interplay between random potentials and random long-range interactions. By mapping the system onto a directed polymer problem, we show that random potentials alone produce correlated energies for the sites in the Fock space, giving rise to the fluctuation growth exponent 1/2. Introducing random long-range interactions alters these correlations and drives the system's fluctuations into the Kardar-Parisi-Zhang universality class in (1+1)D with the exponent 1/3. To validate the universality of the observed fluctuation scaling, we study a complex directed polymer model with competing point and columnar disorder. Our results confirm that columnar disorder corresponds to on-site energies in the Fock space from the random potentials, while point disorder models the effects of random long-range interactions between the two particles. These findings provide new insights into the Fock-space perspective for examining disordered quantum many-body systems, and they emphasize the critical role of disorder structure in determining the universality class of fluctuations in localized quantum systems.

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Phys. Rev. B 112, 014201– Published 2 July, 2025
  • Received 12 February 2025
  • Revised 5 May 2025
  • Accepted 16 June 2025
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