Graph theoretical proof of nonintegrability in quantum many-body systems : Application to the PXP model
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913567506169856 |
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| author | Park, HaRu K. Lee, SungBin |
| author_facet | Park, HaRu K. Lee, SungBin |
| contents | A rigorous proof of integrability or non-integrability in quantum many-body systems is among the most challenging tasks, as it involves demonstrating the presence or absence of local conserved quantities and deciphering the complex dynamics of the system. In this paper, we establish a graph-theoretical analysis as a comprehensive framework for proving the non-integrability of quantum systems. Exemplifying the PXP model, which is widely believed to be non-integrable, this work rigorously proves the absence of local conserved quantities, thereby confirming its non-integrability. This proof for the PXP model gives several important messages not only that the system is non-integrable, but also the quantum many body scaring observed in the model is not associate with the existence of local conserved quantities. From a graph-theoretical perspective, we also highlight its advantage, even in integrable systems, as the classification of local conserved quantities can be achieved by simply counting the number of isolated loops in the graphs. Our new approach is broadly applicable for establishing proofs of (non-)integrability in other quantum many-body systems, significantly simplifying the process of proving nonintegrability and giving numerous potential applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02335 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graph theoretical proof of nonintegrability in quantum many-body systems : Application to the PXP model Park, HaRu K. Lee, SungBin Statistical Mechanics A rigorous proof of integrability or non-integrability in quantum many-body systems is among the most challenging tasks, as it involves demonstrating the presence or absence of local conserved quantities and deciphering the complex dynamics of the system. In this paper, we establish a graph-theoretical analysis as a comprehensive framework for proving the non-integrability of quantum systems. Exemplifying the PXP model, which is widely believed to be non-integrable, this work rigorously proves the absence of local conserved quantities, thereby confirming its non-integrability. This proof for the PXP model gives several important messages not only that the system is non-integrable, but also the quantum many body scaring observed in the model is not associate with the existence of local conserved quantities. From a graph-theoretical perspective, we also highlight its advantage, even in integrable systems, as the classification of local conserved quantities can be achieved by simply counting the number of isolated loops in the graphs. Our new approach is broadly applicable for establishing proofs of (non-)integrability in other quantum many-body systems, significantly simplifying the process of proving nonintegrability and giving numerous potential applications. |
| title | Graph theoretical proof of nonintegrability in quantum many-body systems : Application to the PXP model |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2403.02335 |