Evaluating many-body stabilizer Rényi entropy by sampling reduced Pauli strings: singularities, volume law, and nonlocal magic

• URL: http://arxiv.org/abs/2501.12146v2
• Date: Tue, 18 Feb 2025 11:01:14 GMT
• Title: Evaluating many-body stabilizer Rényi entropy by sampling reduced Pauli strings: singularities, volume law, and nonlocal magic
• Authors: Yi-Ming Ding, Zhe Wang, Zheng Yan,
• Abstract summary: We present a novel quantum Monte Carlo method for evaluating the $alpha$-stabilizer R'enyi entropy (SRE) for any integer $alphage 2$. By interpreting $alpha$-SRE as partition function ratios, we eliminate the sign problem in the imaginary-time path integral. This work provides a powerful tool for exploring the roles of magic in large-scale many-body systems.
• Score: 6.319414487062288
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• Abstract: We present a novel quantum Monte Carlo method for evaluating the $\alpha$-stabilizer R\'enyi entropy (SRE) for any integer $\alpha\ge 2$. By interpreting $\alpha$-SRE as partition function ratios, we eliminate the sign problem in the imaginary-time path integral by sampling reduced Pauli strings within a reduced configuration space, which enables efficient classical computations of $\alpha$-SRE and its derivatives to explore magic in previously inaccessible 2D/higher-dimensional systems. Physically, we first separate the free energy contribution in $2$-SRE. At quantum critical points in 1D/2D transverse field Ising (TFI) models, we reveal nontrivial singularities associated with the characteristic function contribution, directly tied to magic. Their interplay leads to complicated behaviors of $2$-SRE, avoiding extrema at critical points generally. In contrast, by analyzing the volume-law correction of magic, which represents nonlocal magic residing in correlations, we find that its discontinuity is bound to critical properties and would be more useful than the full-state magic. Finally, we verify that $2$-SRE fails to characterize magic in mixed states (e.g. Gibbs states), yielding nonphysical results. This work provides a powerful tool for exploring the roles of magic in large-scale many-body systems, and reveals intrinsic relation between magic and many-body physics.

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