Field Digitization Scaling in a Z_{N}⊂U(1) Symmetric Model.

Area of Science:

• Theoretical Physics
• Computational Physics
• Condensed Matter Physics

Background:

• Simulating quantum field theories requires handling infinite degrees of freedom.
• Field digitization (FD) truncates fields to N discrete values, but lacks a framework for continuum results.

Purpose of the Study:

• To develop a comprehensive framework for analyzing field digitization (FD).
• To interpret the parameter N in FD as a renormalization group (RG) coupling.
• To introduce and apply field digitization scaling (FDS) for obtaining continuum results.

Main Methods:

• Interpreting N in FD as an RG coupling.
• Using effective field theory and RG to derive scaling hypotheses.
• Employing numerical tensor-network calculations.
• Analytical proof relating classical and quantum models.

Main Results:

• Derived generalized scaling hypotheses involving the FD parameter N.
• Uncovered an unconventional universal crossover induced by finite N in a 2D clock model.
• Demonstrated FDS can describe the interplay of bond dimension (χ) and N.
• Proved a direct relation between 2D classical-statistical models and (2+1)D quantum gauge theories.

Conclusions:

• FDS provides a method to relate data from different N-regularized models.
• The study paves the way for FDS applications in quantum simulations of complex models.
• FDS can be a tool for analyzing the continuum limit of digitized quantum field theories.