Mixed-state phase transitions in spin-Holstein models

• URL: http://arxiv.org/abs/2412.02733v1
• Date: Tue, 03 Dec 2024 18:10:10 GMT
• Title: Mixed-state phase transitions in spin-Holstein models
• Authors: Brett Min, Yuxuan Zhang, Yuxuan Guo, Dvira Segal, Yuto Ashida,
• Abstract summary: This work aims to extend the notion of mixed-state phases to the realm of coupled electron/spinphonon systems. We consider a two-dimensional cluster Hamiltonian locally coupled to a set of single bosonic modes with arbitrary coupling strength. We argue that both measures detect signatures of mixed-state phase transitions, albeit at different critical spin-phonon coupling strengths.
• Score: 5.900087161838199
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• Abstract: Understanding coupled electron-phonon systems is one of the fundamental issues in strongly correlated systems. In this work, we aim to extend the notion of mixed-state phases to the realm of coupled electron/spinphonon systems. Specifically, we consider a two-dimensional cluster Hamiltonian locally coupled to a set of single bosonic modes with arbitrary coupling strength. First, we adopt a pure-state framework and examine whether a ground state phase transition out of the symmetry-protected topological phase can be captured using the standard polaron unitary transformation. This approach involves restricting the analysis to the low-energy manifold of the phonon degrees of freedom. We find that the pure-state approach fails to detect the anticipated transition to a topologically trivial phase at strong spin-phonon coupling. Next, we turn to a mixed-state picture. Here, we analyze mixed states of the model obtained by tracing out the phonons degrees of freedom. We employ two distinct diagnostics for mixed-state phase transitions: (i) the von Neumann conditional mutual information (CMI) and (ii) the R\'enyi-2 CMI. We argue that both measures detect signatures of mixed-state phase transitions, albeit at different critical spin-phonon coupling strengths, corresponding to subtly distinct notions of the mixed-state phases.

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