Conformal Dimensions via Large Charge Expansion

Area of Science:

• Quantum Field Theory
• Statistical Mechanics
• Computational Physics

Background:

• Conformal field theories (CFTs) describe critical phenomena but calculating properties like conformal dimensions can be challenging.
• Strongly coupled CFTs with global charges, particularly in the O(2) universality class, lack efficient computational methods.
• The Wilson-Fisher fixed point is a key area of study in critical phenomena.

Purpose of the Study:

• To develop an efficient Monte Carlo algorithm for computing conformal dimensions of large-Q fields.
• To overcome signal-to-noise ratio limitations in such computations.
• To verify a proposed series expansion for conformal dimensions in terms of inverse charge (1/Q).

Main Methods:

• Construction of an efficient Monte Carlo algorithm.
• Accurate computation of conformal dimensions for large-Q fields at the O(2) Wilson-Fisher fixed point.
• Verification of a 1/Q series expansion for conformal dimensions.

Main Results:

• The developed algorithm successfully overcomes signal-to-noise issues.
• Conformal dimensions of large-Q fields were accurately computed.
• The study confirms that conformal dimensions can be obtained via a series expansion in 1/Q.
• The lowest operator's conformal dimensions are predominantly determined by the initial terms of the series.

Conclusions:

• The new Monte Carlo algorithm provides an efficient tool for studying strongly coupled CFTs.
• The findings support the validity of the 1/Q series expansion for conformal dimensions in U(1) charged CFTs.
• This work advances the understanding of critical phenomena and quantum field theory computations.