Entanglement Hamiltonian on subsystem at non-zero temperatures

Abstract: The entanglement Hamiltonian is an effective Hamiltonian that describes the properties of a subsystem after taking the partial trace over the rest of the system. It plays a crucial role in various areas, including clustering of conditional mutual information, Hamiltonian learning, and quantum algorithms, etc [1]. However, determining the structure of the entanglement Hamiltonian is generally a challenging problem. Even at sufficiently high temperatures, the standard cluster expansion method is indicated to be ineffective [2].

In this talk, I will present an alternative approach to studying the entanglement Hamiltonian that works across all temperature regimes. I will also discuss the limitations of this method and its implications for further research.

[1] Tomotaka Kuwahara, Clustering of Conditional Mutual Information and Quantum Markov Structure at Arbitrary Temperatures, Physical Review X 15, 041010 (2025)

[2] Kohtaro Kato, Tomotaka Kuwahara, Clustering of Conditional Mutual Information via Quantum Belief-Propagation Channels, arXiv:2504.02235v2

mathematical physics

Audience: researchers in the discipline

One world IAMP mathematical physics seminar

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