Complete finite-size scaling theory of Renyi thermal entropy for second, first and weak first order quantum phase transitions
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915876048994304 |
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| author | Wang, Zhe Zhu, Yanzhang Ding, Yi-Ming Liu, Zenan Yan, Zheng |
| author_facet | Wang, Zhe Zhu, Yanzhang Ding, Yi-Ming Liu, Zenan Yan, Zheng |
| contents | Establishing the nature of a quantum phase transition in finite-size simulations -- whether continuous, first-order, or weak first-order -- is a fundamental challenge in quantum many-body computation. Especially, the weak first-order phase transition is affected by a super large correlation length and always displays as a continuous critical point in simulated finite-sizes. The core difficulty lies in the fact that there is no effective finite-size theory to distinguish these phase transitions in the realistic simulations limited by the computational resource. In this work, we have fixed this problem by introducing a unified finite-size framework based on the Renyi thermal entropy (RTE) and its derivative (DRTE) to detect and characterize quantum phase transitions. We derive complete scaling theories for the RTE and DRTE at second-order, first-order, and weak first-order transitions, showing that the DRTE naturally isolates the singular part of the free energy and strengthens the characteristics of various phase transitions in finite sizes. Using quantum Monte Carlo simulations, we demonstrate accurate data collapse and extraction of critical exponents at (2+1)-dimensional O($N$) critical points. More importantly, the DRTE provides a smoking-gun signature of weak first-order transitions through a clear double-peak structure and a crossing at zero, which we unambiguously observe in debated deconfined quantum criticality candidates such as the $J$--$Q$ models. Our approach offers a general, unbiased, and numerically efficient tool for probing the universal properties of quantum phase transitions, resolving long-standing ambiguities between continuous and weak first-order scenarios. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_16111 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complete finite-size scaling theory of Renyi thermal entropy for second, first and weak first order quantum phase transitions Wang, Zhe Zhu, Yanzhang Ding, Yi-Ming Liu, Zenan Yan, Zheng Strongly Correlated Electrons Statistical Mechanics Computational Physics Establishing the nature of a quantum phase transition in finite-size simulations -- whether continuous, first-order, or weak first-order -- is a fundamental challenge in quantum many-body computation. Especially, the weak first-order phase transition is affected by a super large correlation length and always displays as a continuous critical point in simulated finite-sizes. The core difficulty lies in the fact that there is no effective finite-size theory to distinguish these phase transitions in the realistic simulations limited by the computational resource. In this work, we have fixed this problem by introducing a unified finite-size framework based on the Renyi thermal entropy (RTE) and its derivative (DRTE) to detect and characterize quantum phase transitions. We derive complete scaling theories for the RTE and DRTE at second-order, first-order, and weak first-order transitions, showing that the DRTE naturally isolates the singular part of the free energy and strengthens the characteristics of various phase transitions in finite sizes. Using quantum Monte Carlo simulations, we demonstrate accurate data collapse and extraction of critical exponents at (2+1)-dimensional O($N$) critical points. More importantly, the DRTE provides a smoking-gun signature of weak first-order transitions through a clear double-peak structure and a crossing at zero, which we unambiguously observe in debated deconfined quantum criticality candidates such as the $J$--$Q$ models. Our approach offers a general, unbiased, and numerically efficient tool for probing the universal properties of quantum phase transitions, resolving long-standing ambiguities between continuous and weak first-order scenarios. |
| title | Complete finite-size scaling theory of Renyi thermal entropy for second, first and weak first order quantum phase transitions |
| topic | Strongly Correlated Electrons Statistical Mechanics Computational Physics |
| url | https://arxiv.org/abs/2506.16111 |