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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2501.12146 |
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| _version_ | 1866909613915373568 |
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| author | Ding, Yi-Ming Wang, Zhe Yan, Zheng |
| author_facet | Ding, Yi-Ming Wang, Zhe Yan, Zheng |
| contents | We present a novel quantum Monte Carlo method for evaluating the $α$-stabilizer Rényi entropy (SRE) for any integer $α\ge 2$. By interpreting $α$-SRE as partition function ratios, we eliminate the sign problem in the imaginary-time path integral by sampling \emph{reduced Pauli strings} within a \emph{reduced configuration space}, which enables efficient classical computations of $α$-SRE and its derivatives to explore magic in previously inaccessible 2D/higher-dimensional systems. We first isolate the free energy part in $2$-SRE, which is a trivial term. Notably, at quantum critical points in 1D/2D transverse field Ising (TFI) models, we reveal nontrivial singularities associated with the \emph{characteristic function} contribution, directly tied to magic. Their interplay leads to complicated behaviors of $2$-SRE, avoiding extrema at critical points generally. In contrast, analyzing the volume-law correction to SRE reveals a discontinuity tied to criticalities, suggesting that it is more informative than the full-state magic. For conformal critical points, we claim it could reflect nonlocal magic residing in correlations. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12146 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Evaluating many-body stabilizer Rényi entropy by sampling reduced Pauli strings: singularities, volume law, and nonlocal magic Ding, Yi-Ming Wang, Zhe Yan, Zheng Quantum Physics Strongly Correlated Electrons Computational Physics Data Analysis, Statistics and Probability We present a novel quantum Monte Carlo method for evaluating the $α$-stabilizer Rényi entropy (SRE) for any integer $α\ge 2$. By interpreting $α$-SRE as partition function ratios, we eliminate the sign problem in the imaginary-time path integral by sampling \emph{reduced Pauli strings} within a \emph{reduced configuration space}, which enables efficient classical computations of $α$-SRE and its derivatives to explore magic in previously inaccessible 2D/higher-dimensional systems. We first isolate the free energy part in $2$-SRE, which is a trivial term. Notably, at quantum critical points in 1D/2D transverse field Ising (TFI) models, we reveal nontrivial singularities associated with the \emph{characteristic function} contribution, directly tied to magic. Their interplay leads to complicated behaviors of $2$-SRE, avoiding extrema at critical points generally. In contrast, analyzing the volume-law correction to SRE reveals a discontinuity tied to criticalities, suggesting that it is more informative than the full-state magic. For conformal critical points, we claim it could reflect nonlocal magic residing in correlations. 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. |
| title | Evaluating many-body stabilizer Rényi entropy by sampling reduced Pauli strings: singularities, volume law, and nonlocal magic |
| topic | Quantum Physics Strongly Correlated Electrons Computational Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2501.12146 |