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Debasish Banerjee1, Shailesh Chandrasekharan2, Domenico Orlando3,4

  • 1NIC, DESY, Platanenallee 6, D-15738 Zeuthen, Germany.

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|February 27, 2018
PubMed
Summary
This summary is machine-generated.

We developed a new Monte Carlo algorithm to accurately compute conformal dimensions for large-Q fields in the O(2) universality class. This method verifies that conformal dimensions depend on a series expansion in the inverse charge (1/Q).

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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.