Triangle Nuclear Theory - Asymptotic Freedom via Qubit Regularization: A new RG perspective
Shailesh Chandrasekharan (Duke U.) Asymptotically free quantum field theories (AFQFT) emerge non-perturbatively in the continuum despite the infinities that are plagued in perturbative calculations. Wilson's RG provides a framework to understand this feature of AFQFT starting from a lattice regularization, which however begins with the assumption that the local Hilbert space on the lattice is infinite dimensional so that the UV fixed point is preserved. However, recent effort in formulating these theories on a quantum computer forces one to look for lattice theories with a finite local Hilbert space. We refer to this as the "qubit regularization" of a QFT. Does the finite local Hilbert space necessarily destroy the UV fixed point, or can it be recovered via RG? Recent results suggest that the latter is true at least in some cases, where the AFQFT arises at a quantum critical point in a theory with a finite local Hilbert space. However, the RG flow is quite exotic in these cases. We will use the well-known BKT transition as an example to show this non-trivial RG flow.