Sampling versus Blocking

TL;DR

This paper compares traditional blocking methods and modern Tensor RG techniques in lattice models, highlighting recent advances in fixed point searches, critical exponent calculations, and sign problem resolutions.

Contribution

It introduces recent results using Tensor RG methods for lattice models, demonstrating improvements over conventional blocking and sampling approaches.

Findings

Tensor RG achieves better accuracy in critical exponent calculations.

Tensor RG effectively resolves sign problems in certain models.

Blocking methods have smaller statistical but larger systematic errors.

Abstract

The idea of blocking in configuration space has played an important role in the development of the RG ideas. However, despite being half a century old and having had a huge intellectual impact, generic numerical methods to perform blocking for lattice models have progressed more slowly than sampling methods. Blocking may be essential to deal with near conformal situations. Typically, blocking methods have smaller statistical errors but larger systematic errors than sampling methods. This situation is evolving with recent developments based on the Tensor RG (TRG) method. We report recent results for spin and gauge lattice models obtained with this new method regarding searches for fixed points, calculations of critical exponents and resolutions of sign problems. An interesting model for comparison is the 2-dimensional O(2) model with a chemical potential which has a sign problem with conventional Monte Carlo but allows sampling with the worm algorithm and blocking with various TRG formulations. We compare the efficiency and accuracy of these two methods.