多体Aubry-André模型中的斐波那契数系与局域化判据
Fibonacci number systems and the localization criterion in the many-body Aubry-André model
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中文总结 AI 辅助
本文提出分数斐波那契数系，将其用于解释多体非相互作用Aubry-André模型的局域化相图，得到有限及热力学极限下的局域化判据，并讨论了热力学极限的性质。
中文摘要 AI 辅助
我们引入了一种斐波那契数系的扩展形式，将其命名为分数斐波那契数系，该数系可用于在用于表示自然数的斐波那契数系与可表示实数的无理基φ数系之间插值。该数系可用于解释多体非相互作用Aubry-André模型的局域化相图。对于有限系统尺寸，若将粒子密度表示为分数斐波那契数系，则可得到局域化判据；在热力学极限下，该判据仍然成立，此时粒子密度以基φ形式表示，本文还讨论了热力学极限的性质。
英文摘要
We introduce an extension of the Fibonacci number system, we call the fractional Fibonacci number system, which interpolates between the Fibonacci number system (used for natural numbers) and the irrational base-$ϕ$ number system, which can be used to represent real numbers. The number system finds its use in interpreting the localization phase diagram of the many-body non-interacting Aubry-André model. For finite system sizes a localization criterion can be obtained if the particle density is written in the fractional Fibonacci number system. In the thermodynamic limit, the criterion remains, but in this case the particle density is expressed in base-$ϕ$. The nature of the thermodynamic limit is also discussed.
