Quantum Fisher Information Reveals UV-IR Mixing in the Strange Metal

• URL: http://arxiv.org/abs/2412.14413v1
• Date: Wed, 18 Dec 2024 23:46:22 GMT
• Title: Quantum Fisher Information Reveals UV-IR Mixing in the Strange Metal
• Authors: David Bałut, Xuefei Guo, Niels de Vries, Dipanjan Chaudhuri, Barry Bradlyn, Peter Abbamonte, Philip W. Phillips,
• Abstract summary: We compute the resultant quantum Fisher information (QFI), a witness to multi-partite entanglement. As this constant depends on both UV and IR properties, it illustrates that multipartite entanglement in a strange metal exhibits UV-IR mixing.
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• Abstract: The density-density response in optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ has recently been shown to exhibit conformal symmetry. Using, the experimentally inferred conformal dynamic susceptibility, we compute the resultant quantum Fisher information (QFI), a witness to multi-partite entanglement. In contrast to a Fermi liquid in which the QFI is approximately temperature independent much below the Fermi energy scale, we find that the QFI increases as a power law at low temperatures but ultimately extrapolates to a constant at $T=0$. The constant is of the form, $\omega_g^{2\Delta}$, where $\Delta$ is the conformal dimension and $\omega_g$ is the UV cutoff which is on the order of the pseudogap. As this constant {depends on both UV and IR properties}, it illustrates that multipartite entanglement in a strange metal exhibits UV-IR mixing, a benchmark feature of doped Mott insulators as exemplified by dynamical spectral weight transfer. We conclude with a discussion of the implication of our results for low-energy reductions of the Hubbard model.

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