2025/07/30 by Calliari, Gabriele, Ott, Robert, Pichler, Hannes +1 · 4 citations
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2507.22984
The simulation of quantum field theories, both classical and quantum, requires regularization of infinitely many degrees of freedom. However, in the context of field digitization (FD) -- a truncation of the local fields to N discrete values -- a comprehensive framework to obtain continuum results is currently missing. Here, we propose to analyze FD by interpreting the parameter N as a coupling in the renormalization group (RG) sense. As a first example, we investigate the two-dimensional classical N-state clock model as a ℤN FD of the U(1)-symmetric XY-model. Using effective field theory, we employ the RG to derive generalized scaling hypotheses involving the FD parameter N, which allows us to relate data obtained for different N-regularized models in a procedure that we term field digitization scaling (FDS). Using numerical tensor-network calculations at finite bond dimension χ, we further uncover an unconventional universal crossover around a low-temperature phase transition induced by finite N, demonstrating that FDS can be extended to describe the interplay of χ and N. Finally, we analytically prove that our calculations for the 2D classical-statistical ℤN clock model are directly related to the quantum physics in the ground state of a (2+1)D ℤN lattice gauge theory which serves as a FD of compact quantum electrodynamics. Our study thus paves the way for applications of FDS to quantum simulations of more complex models in higher spatial dimensions, where it could serve as a tool to analyze the continuum limit of digitized quantum field theories.