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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2412.09905 |
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| _version_ | 1866917247237226496 |
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| author | Lin, Feng-Li Hong, Jhh-Jing Huang, Ching-Yu |
| author_facet | Lin, Feng-Li Hong, Jhh-Jing Huang, Ching-Yu |
| contents | We consider the thermalization hypothesis of pure states in quantum Ising chain with $Z_2$ symmetry, XXZ chain with $U(1)$ symmetry, and XXX chain with $SU(2)$ symmetries. Two kinds of pure states are considered: the energy eigenstates and the typical states evolved unitarily from the random product states for a long enough period. We further group the typical states by their expectation values of the conserved charges and consider the fine-grained thermalization hypothesis. We compare the locally (subsystem) reduced states of typical states/eigenstates with the ones of the corresponding thermal ensemble states. Besides the usual thermal ensembles such as the (micro-)canonical ensemble without conserved charges and the generalized Gibbs ensemble (GGE) with all conserved charges included, we also consider the so-called partial-GGEs (p-GGEs), which include only part of the conserved charges in the thermal ensemble. Moreover, in the framework of p-GGE, the Hamiltonian and other conserved charges are on an equal footing. The introduction of p-GGEs extends quantum thermalization to a more general scope. The validity of the subsystem thermalization hypothesis can be quantified by the smallness of the relative entropy of the reduced states obtained from the GGE/p-GGE and the typical states/eigenstates. We examine the validity of the thermalization hypothesis by numerically studying the relative entropy demographics. We show that the thermalization hypothesis holds generically for the small enough subsystems for various p-GGEs. Thus, our framework extends the universality of quantum thermalization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09905 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subsystem Thermalization Hypothesis in Quantum Spin Chains with Conserved Charges Lin, Feng-Li Hong, Jhh-Jing Huang, Ching-Yu Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory We consider the thermalization hypothesis of pure states in quantum Ising chain with $Z_2$ symmetry, XXZ chain with $U(1)$ symmetry, and XXX chain with $SU(2)$ symmetries. Two kinds of pure states are considered: the energy eigenstates and the typical states evolved unitarily from the random product states for a long enough period. We further group the typical states by their expectation values of the conserved charges and consider the fine-grained thermalization hypothesis. We compare the locally (subsystem) reduced states of typical states/eigenstates with the ones of the corresponding thermal ensemble states. Besides the usual thermal ensembles such as the (micro-)canonical ensemble without conserved charges and the generalized Gibbs ensemble (GGE) with all conserved charges included, we also consider the so-called partial-GGEs (p-GGEs), which include only part of the conserved charges in the thermal ensemble. Moreover, in the framework of p-GGE, the Hamiltonian and other conserved charges are on an equal footing. The introduction of p-GGEs extends quantum thermalization to a more general scope. The validity of the subsystem thermalization hypothesis can be quantified by the smallness of the relative entropy of the reduced states obtained from the GGE/p-GGE and the typical states/eigenstates. We examine the validity of the thermalization hypothesis by numerically studying the relative entropy demographics. We show that the thermalization hypothesis holds generically for the small enough subsystems for various p-GGEs. Thus, our framework extends the universality of quantum thermalization. |
| title | Subsystem Thermalization Hypothesis in Quantum Spin Chains with Conserved Charges |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.09905 |