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引用次数: 0
摘要
我们构建了一个具有守恒U(1)电荷的近CFT1模型族,其基本自由度是典型玻色子。萨奇德夫-叶-基塔耶夫(SYK)模型是第一个实现近 CFT1 动力学的微观模型,它基于费米子之间的随机 p 局域相互作用。然而,在 p 局域方法中,玻色子近 CFT1 模型仍然难以捉摸,因为这种构造在低温下通常会出现不需要的有序性。我们的构造基于最近的一个见解,即如果我们在多体 Fock 空间中放置大量随机通量,而 p 局域性并不是必要的,那么近 CFT1 动力学一般都能产生。无论底层自由度的性质如何,所有这些模型本质上都是通过弦图求解的。我们进一步论证,这类玻色模型不会出现能量不稳定性或不必要的低温有序性。为了进行比较,我们还考虑了基于量子比特的第二类电荷守恒模型。这些模型的热力学标度与双标度复 SYK 模型非常相似,但没有后者的某些奇异性。我们还表明,这两种模型的能级统计都是通过随机矩阵理论的普遍性来描述的,直到非常低的能量。
We construct a family of near-CFT1 models with a conserved U(1) charge, whose basic degrees of freedom are canonical bosons. The Sachdev-Ye-Kitaev (SYK) model — the first microscopic model that realizes the near-CFT1 dynamics — is based on random p-local interactions among fermions. However, a bosonic near-CFT1 model has remained elusive in the p-local approach because such constructions generally suffer from unwanted orderings at low temperatures. Our construction is based on a recent insight that near-CFT1 dynamics can quite generally arise if we place a large amount of random fluxes in a many-body Fock space and p-locality is not essential. All such models are essentially solved by chord diagrams regardless of the nature of the underlying degrees of freedom. We further argue that such bosonic models do not suffer from energetic instablities or unwanted low-temperature orderings. For comparison we also consider a second class of charge-conserving models which are based on qubits. The thermodynamic scalings of these models are very similar to those of the double-scaled complex SYK model but are free of certain singularities the latter suffers from. We also show the level statistics of both models are described by random matrix theory universality down to very low energies.
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