Worldline Monte Carlo for fermion models at large N_f
arXiv:0903.4421 · doi:10.1088/1126-6708/2009/08/010
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.
40 pages, 13 figures
References in corpus (12)
- Color superconductivity in dense quark matter
- Worldline Instantons II: The Fluctuation Prefactor
- Inhomogeneous Condensates in the Thermodynamics of the Chiral NJL_2 model
- Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems
- Worldline algorithms for Casimir configurations
- Deconfinement in dense 2-color QCD
- A Twisted Kink Crystal in the Chiral Gross-Neveu model
- Casimir edge effects
- Solving two-dimensional large-N QCD with a nonzero density of baryons and arbitrary quark mass
- Worldline Approach To The Casimir Effect
- New baryon matter in the lattice Gross-Neveu model
- Worldline Approach to Chiral Fermions
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