Efficient simulation of relativistic fermions via vertex models

Abstract

We have developed an efficient simulation algorithm for strongly interacting relativistic fermions in two-dimensional field theories based on a formulation as a loop gas. The loop models describing the dynamics of the fermions can be mapped to statistical vertex models and our proposal is in fact an efficient simulation algorithm for generic vertex models in arbitrary dimensions. The algorithm essentially eliminates critical slowing down by sampling two-point correlation functions and it allows simulations directly in the massless limit. Moreover, it generates loop configurations with fluctuating topological boundary conditions enabling to simulate fermions with arbitrary periodic or anti-periodic boundary conditions. As illustrative examples, the algorithm is applied to the Gross-Neveu model and to the Schwinger model in the strong coupling limit.

5 pages, 4 figures

References in corpus (11)

• Quantum Monte Carlo with Directed Loops
• Cluster Algorithm for Vertex Models
• Worm algorithms for classical statistical models
• Chiral Limit of Strongly Coupled Lattice Gauge Theories
• Cluster simulation of relativistic fermions in two space-time dimensions
• Simulating the All-Order Hopping Expansion II: Wilson Fermions
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• The lattice Schwinger model as a discrete sum of filled Wilson loops
• The exact equivalence of the two-flavour strong coupling lattice Schwinger model with Wilson fermions to a vertex model
• The exact equivalence of the one-flavour lattice Thirring model with Wilson fermions to a two-colour loop model

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