Abstract
The dual form of the massless Schwinger model on the lattice overcomes the complex action problems from two sources: a topological term, as well as non-zero chemical potential, making these physically interesting cases accessible to Monte Carlo simulations. The partition function is represented as a sum over fermion loops, dimers and plaquette-surfaces such that all contributions are real and positive. However, these new variables constitute a highly constrained system and suitable update strategies have to be developed. In this exploratory study we present an approach based on locally growing plaquette-surfaces surrounded by fermion loop segments combined with a worm based strategy for updating chains of dimers, as well as winding fermion loops. The update strategy is checked with conventional simulations as well as reference data from exact summation on small volumes and we discuss some physical implications of the results.
Highlights
Calculations at finite density are considered to be one of the great challenges for lattice field theory Monte Carlo simulations
The chemical potential, as well as the topological term lead to complex action problems and the dual representation in terms of world-lines, dimers and world-sheets given in [8] solves both these problems in principle by providing an exact representation where all contributions to the partition sum are real and positive
The results presented here constitute the first simulation of the Schwinger model at arbitrary, i.e., weak couplings with a finite chemical potential and a topological term
Summary
Calculations at finite density are considered to be one of the great challenges for lattice field theory Monte Carlo simulations. The chemical potential, as well as the topological term lead to complex action problems and the dual representation in terms of world-lines, dimers and world-sheets given in [8] solves both these problems in principle by providing an exact representation where all contributions to the partition sum are real and positive In this exploratory paper we present strategies for simulating the dual representation [8]. The reference data for the Schwinger model which can be obtained from the dual approach tested here, will be useful for assessing other techniques that are explored for overcoming complex action problems: In particular methods based on complexification (see, e.g., the reviews [9]) or new strategies for simulating systems at finite vacuum term [10] can be cross-checked against results from the world-line/world-sheet methods presented here
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