Universal fluctuations of localized two interacting particles in one dimension

• URL: http://arxiv.org/abs/2502.01399v1
• Date: Mon, 03 Feb 2025 14:30:19 GMT
• Title: Universal fluctuations of localized two interacting particles in one dimension
• Authors: Sen Mu, Gabriel Lemarié, Jiangbin Gong,
• Abstract summary: We investigate the universal fluctuations of localized wavefunction in the Fock space of two interacting particles in one-dimensional disordered systems. 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.
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• Abstract: We investigate the universal fluctuations of localized wavefunction 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 emphasize the critical role of disorder structure in determining the universality class of fluctuations in localized quantum systems.

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