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

• URL: http://arxiv.org/abs/2605.24645v1
• Date: Sat, 23 May 2026 16:21:21 GMT
• Title: Geometric phases of reduced states in the transverse-field Ising chain
• Abstract summary: We examine two geometric phases defined for mixed quantum states$-$the interferometric geometric phase and the Uhlmann phase.<n>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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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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