Subsystem Thermalization Hypothesis in Quantum Spin Chains with Conserved Charges

• URL: http://arxiv.org/abs/2412.09905v1
• Date: Fri, 13 Dec 2024 06:45:07 GMT
• Title: Subsystem Thermalization Hypothesis in Quantum Spin Chains with Conserved Charges
• Authors: Feng-Li Lin, Jhh-Jing Hong, Ching-Yu Huang,
• Abstract summary: We consider the thermalization hypothesis of pure states in quantum Ising chain with $Z$ symmetry, XXZ chain with $U(1)$ symmetry, and XXX chain with $SU(2)$ symmetries.
• Score: 0.020482269513546456
• License:
• Abstract: 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.

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