Solvable Random Unitary Dynamics in a Disordered Tomonaga-Luttinger Liquid
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arXiv
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| Format: | Preprint |
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2026
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| author | Zhou, Tian-Gang Giamarchi, Thierry |
| author_facet | Zhou, Tian-Gang Giamarchi, Thierry |
| contents | Disordered one-dimensional interacting systems have long been characterized via conventional correlation functions. A complementary quantum-information perspective quantifies the randomness of the unitary ensemble dynamics generated by a quantum system through the frame potential, which serves as a practical diagnostic for quantum algorithmic performance. However, no analytical treatment has yet been achieved for experimentally accessible interacting one-dimensional systems. In this Letter, we derive a closed-form expression for the frame potential of a Tomonaga-Luttinger liquid with quenched Gaussian forward-scattering disorder. Exploiting the exactly quadratic structure of the disorder-averaged Keldysh action, we show that the frame potential decays as a power law at early times and saturates to a late-time plateau controlled by a single coupling parameter. Taking the random field XXZ spin chain as a specific microscopic realization, we show that the strongest randomness is achieved near the Heisenberg ferromagnetic point and can be exponentially enhanced through a multiple-quench protocol. We validate our results across the entire gapless phase, with direct implications for algorithm design in analog quantum simulation platforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25995 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solvable Random Unitary Dynamics in a Disordered Tomonaga-Luttinger Liquid Zhou, Tian-Gang Giamarchi, Thierry Quantum Physics Disordered Systems and Neural Networks Quantum Gases Statistical Mechanics Strongly Correlated Electrons Disordered one-dimensional interacting systems have long been characterized via conventional correlation functions. A complementary quantum-information perspective quantifies the randomness of the unitary ensemble dynamics generated by a quantum system through the frame potential, which serves as a practical diagnostic for quantum algorithmic performance. However, no analytical treatment has yet been achieved for experimentally accessible interacting one-dimensional systems. In this Letter, we derive a closed-form expression for the frame potential of a Tomonaga-Luttinger liquid with quenched Gaussian forward-scattering disorder. Exploiting the exactly quadratic structure of the disorder-averaged Keldysh action, we show that the frame potential decays as a power law at early times and saturates to a late-time plateau controlled by a single coupling parameter. Taking the random field XXZ spin chain as a specific microscopic realization, we show that the strongest randomness is achieved near the Heisenberg ferromagnetic point and can be exponentially enhanced through a multiple-quench protocol. We validate our results across the entire gapless phase, with direct implications for algorithm design in analog quantum simulation platforms. |
| title | Solvable Random Unitary Dynamics in a Disordered Tomonaga-Luttinger Liquid |
| topic | Quantum Physics Disordered Systems and Neural Networks Quantum Gases Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2604.25995 |