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arXiv · 2605.24645

Geometric phases of reduced states in the transverse-field Ising chain

Chiragkumar R. Vasani·Erik Sjöqvist
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Abstract

Geometric phases have been extensively investigated in a wide range of quantum systems, often revealing deep connections to the underlying topology of many-body states. In this work, we examine two geometric phases defined for mixed quantum states$-$the interferometric geometric phase and the Uhlmann phase$-$extracted from two-site reduced density matrices of the transverse-field Ising model with nearest-neighbor interacting spins. By applying coordinated local unitary rotations to the spins, we compute the geometric phases associated with the two-site states across the critical point. We find that the interferometric phase is a more reliable indicator of the quantum phase transition in this model than the Uhlmann phase.

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Chiragkumar R. Vasani, Erik Sjöqvist. 2026-05-23. Geometric phases of reduced states in the transverse-field Ising chain. https://arxiv.org/abs/2605.24645

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