Worldline Monte Carlo for fermion models at large N_f

TL;DR

This paper investigates the application of worldline Monte Carlo methods to strongly-coupled fermionic systems at large N_f, demonstrating advantages like absence of fermion doubling and maintaining chiral symmetry, while also discussing limitations such as convergence issues.

Contribution

It introduces a worldline Monte Carlo approach for fermionic models at large N_f, highlighting its benefits and analyzing potential computational challenges.

Findings

Fermion doubling problems are avoided with worldline Monte Carlo.

Chiral symmetry can be maintained explicitly in the approach.

Potential convergence issues arise with fermionic zero modes and high-density regimes.

Abstract

Strongly-coupled fermionic systems can support a variety of low-energy phenomena, giving rise to collective condensation, symmetry breaking and a rich phase structure. We explore the potential of worldline Monte Carlo methods for analyzing the effective action of fermionic systems at large flavor number N_f, using the Gross-Neveu model as an example. Since the worldline Monte Carlo approach does not require a discretized spacetime, fermion doubling problems are absent, and chiral symmetry can manifestly be maintained. As a particular advantage, fluctuations in general inhomogeneous condensates can conveniently be dealt with analytically or numerically, while the renormalization can always be uniquely performed analytically. We also critically examine the limitations of a straightforward implementation of the algorithms, identifying potential convergence problems in the presence of fermionic zero modes as well as in the high-density region.