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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.02567 |
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| _version_ | 1866908477987749888 |
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| author | Lloyd, Jerome Abanin, Dmitry A. Gopalakrishnan, Sarang |
| author_facet | Lloyd, Jerome Abanin, Dmitry A. Gopalakrishnan, Sarang |
| contents | The Markov length was recently proposed as an information-theoretic diagnostic for quantum mixed-state phase transitions [Sang & Hsieh, Phys. Rev. Lett. 134, 070403 (2025)]. Here, we show that the Markov length diverges even under classical stochastic dynamics, when a low-temperature ordered state is quenched into the high temperature phase. Conventional observables do not exhibit growing length scales upon quenching into the high-temperature phase; however, the Markov length grows exponentially in time. Consequently, the state of a system as it heats becomes increasingly non-Gibbsian, and the range of its putative "parent Hamiltonian" must diverge with the Markov length. From this information-theoretic point of view the late-time limit of thermalization is singular. We introduce a numerical technique for computing the Markov length based on matrix-product states, and explore its dynamics under general thermal quenches in the one-dimensional classical Ising model. For all cases, we provide simple information-theoretic arguments that explain our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02567 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diverging conditional correlation lengths in the approach to high temperature Lloyd, Jerome Abanin, Dmitry A. Gopalakrishnan, Sarang Quantum Physics Statistical Mechanics The Markov length was recently proposed as an information-theoretic diagnostic for quantum mixed-state phase transitions [Sang & Hsieh, Phys. Rev. Lett. 134, 070403 (2025)]. Here, we show that the Markov length diverges even under classical stochastic dynamics, when a low-temperature ordered state is quenched into the high temperature phase. Conventional observables do not exhibit growing length scales upon quenching into the high-temperature phase; however, the Markov length grows exponentially in time. Consequently, the state of a system as it heats becomes increasingly non-Gibbsian, and the range of its putative "parent Hamiltonian" must diverge with the Markov length. From this information-theoretic point of view the late-time limit of thermalization is singular. We introduce a numerical technique for computing the Markov length based on matrix-product states, and explore its dynamics under general thermal quenches in the one-dimensional classical Ising model. For all cases, we provide simple information-theoretic arguments that explain our results. |
| title | Diverging conditional correlation lengths in the approach to high temperature |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2508.02567 |