Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917186884337664 |
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| author | Yu, Yin-Kai Li, Zhi-Xuan Yin, Shuai Li, Zi-Xiang |
| author_facet | Yu, Yin-Kai Li, Zhi-Xuan Yin, Shuai Li, Zi-Xiang |
| contents | The notorious fermion sign problem, arising from fermion statistics, presents a fundamental obstacle to the numerical simulation of quantum many-body systems. Here, we introduce a framework that circumvents the sign problem in the studies of quantum criticality and its associated phases by leveraging imaginary-time nonequilibrium critical dynamics. We demonstrate that the critical properties can be accurately determined from the system's short-time relaxation, a regime where the sign problem remains manageable for quantum Monte-Carlo (QMC) simulations. After validating this approach on two benchmark fermionic models, we apply it to the sign-problematic Hubbard model hosting SU(3)-symmetric Dirac fermions. We present the first numerically exact characterization of its quantum phase diagram, revealing a continuous transition between a Dirac semi-metal and a SU(3) antiferromagnetic phase. This transition defines an unconventional Gross-Neveu universality class that fundamentally reshapes current understanding of Gross-Neveu criticality. Our work provides a powerful tool for investigating sign-problematic systems and quantum criticality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time Yu, Yin-Kai Li, Zhi-Xuan Yin, Shuai Li, Zi-Xiang Strongly Correlated Electrons Statistical Mechanics Quantum Physics The notorious fermion sign problem, arising from fermion statistics, presents a fundamental obstacle to the numerical simulation of quantum many-body systems. Here, we introduce a framework that circumvents the sign problem in the studies of quantum criticality and its associated phases by leveraging imaginary-time nonequilibrium critical dynamics. We demonstrate that the critical properties can be accurately determined from the system's short-time relaxation, a regime where the sign problem remains manageable for quantum Monte-Carlo (QMC) simulations. After validating this approach on two benchmark fermionic models, we apply it to the sign-problematic Hubbard model hosting SU(3)-symmetric Dirac fermions. We present the first numerically exact characterization of its quantum phase diagram, revealing a continuous transition between a Dirac semi-metal and a SU(3) antiferromagnetic phase. This transition defines an unconventional Gross-Neveu universality class that fundamentally reshapes current understanding of Gross-Neveu criticality. Our work provides a powerful tool for investigating sign-problematic systems and quantum criticality. |
| title | Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time |
| topic | Strongly Correlated Electrons Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2410.18854 |