截断西格玛模型的普适性
Universality of a truncated sigma-model
摘要：
玻色子量子场论，即使使用有限格点正则化，也具有无限维希尔伯特空间，因此不能在具有有限数量量子比特的量子计算机中模拟。然后需要截断希尔伯特空间，并在双重极限之后获得物理结果：一个是去除截断，另一个是去除调节器（连续极限）。一个更简单的替代方法是找到一个有限维希尔伯特空间的模型，该空间与连续统模型属于同一普适类（“量子化”），因此只需要空间连续极限。一个量子化的$1+1$维渐近自由的$O(3)$非线性$σ$ -模型的基础上的思想的非对易几何arXiv：1903.06577，在本文中，我们提供的证据表明，它再现物理的$σ$ -模型在红外和紫外区。
英文摘要：
Bosonic quantum field theories, even when regularized using a finite lattice, possess an infinite dimensional Hilbert space and, therefore, cannot be simulated in quantum computers with a finite number of qubits. A truncation of the Hilbert space is then needed and the physical results are obtained after a double limit: one to remove the truncation and another to remove the regulator (the continuum limit). A simpler alternative is to find a model with a finite dimensional Hilbert space belonging to the same universality class as the continuum model (a "qubitization"), so only the space continuum limit is required. A qubitization of the $1+1$ dimensional asymptotically free $O(3)$ nonlinear $σ$-model based on ideas of non-commutative geometry was previously proposed arXiv:1903.06577 and, in this paper, we provide evidence that it reproduces the physics of the $σ$-model both in the infrared and the ultraviolet regimes.
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