Universal fluctuations of localized two interacting particles in one dimension
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916823327309824 |
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| author | Mu, Sen Lemarié, Gabriel Gong, Jiangbin |
| author_facet | Mu, Sen Lemarié, Gabriel Gong, Jiangbin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01399 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal fluctuations of localized two interacting particles in one dimension Mu, Sen Lemarié, Gabriel Gong, Jiangbin Disordered Systems and Neural Networks Quantum Gases Statistical Mechanics Quantum Physics 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. |
| title | Universal fluctuations of localized two interacting particles in one dimension |
| topic | Disordered Systems and Neural Networks Quantum Gases Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2502.01399 |